diff --git a/swh/deposit/api/checks.py b/swh/deposit/api/checks.py
--- a/swh/deposit/api/checks.py
+++ b/swh/deposit/api/checks.py
@@ -19,11 +19,10 @@
 from typing import Dict, Optional, Tuple
 from xml.etree import ElementTree
 
-import iso8601
 import pkg_resources
 import xmlschema
 
-from swh.deposit.utils import NAMESPACES, normalize_date, parse_swh_metadata_provenance
+from swh.deposit.utils import NAMESPACES, parse_swh_metadata_provenance
 
 MANDATORY_FIELDS_MISSING = "Mandatory fields are missing"
 INVALID_DATE_FORMAT = "Invalid date format"
@@ -35,6 +34,7 @@
 @dataclasses.dataclass
 class Schemas:
     swh: xmlschema.XMLSchema11
+    codemeta: xmlschema.XMLSchema11
 
 
 @functools.lru_cache(1)
@@ -44,7 +44,7 @@
             pkg_resources.resource_string("swh.deposit", f"xsd/{name}.xsd").decode()
         )
 
-    return Schemas(swh=load_xsd("swh"))
+    return Schemas(swh=load_xsd("swh"), codemeta=load_xsd("codemeta"))
 
 
 def check_metadata(metadata: ElementTree.Element) -> Tuple[bool, Optional[Dict]]:
@@ -93,25 +93,21 @@
         except xmlschema.exceptions.XMLSchemaException as e:
             return False, {"metadata": [{"fields": ["swh:deposit"], "summary": str(e)}]}
 
-    fields = []
-
-    for commit_date in metadata.findall(
-        "codemeta:datePublished", namespaces=NAMESPACES
-    ):
-        try:
-            normalize_date(commit_date.text)
-        except iso8601.iso8601.ParseError:
-            fields.append("codemeta:datePublished")
-
-    for author_date in metadata.findall("codemeta:dateCreated", namespaces=NAMESPACES):
+    detail = []
+    for child in metadata:
+        for schema_element in schemas().codemeta.root_elements:
+            if child.tag in schema_element.name:
+                break
+        else:
+            # Tag is not specified in the schema, don't validate it
+            continue
         try:
-            normalize_date(author_date.text)
-        except iso8601.iso8601.ParseError:
-            fields.append("codemeta:dateCreated")
+            schemas().codemeta.validate(child)
+        except xmlschema.exceptions.XMLSchemaException as e:
+            detail.append({"fields": [schema_element.prefixed_name], "summary": str(e)})
 
-    if fields:
-        detail = [{"summary": INVALID_DATE_FORMAT, "fields": fields}]
-        return False, {"metadata": detail + suggested_fields}
+    if detail:
+        return False, {"metadata": detail}
 
     if suggested_fields:  # it's fine but warn about missing suggested fields
         return True, {"metadata": suggested_fields}
diff --git a/swh/deposit/tests/api/test_checks.py b/swh/deposit/tests/api/test_checks.py
--- a/swh/deposit/tests/api/test_checks.py
+++ b/swh/deposit/tests/api/test_checks.py
@@ -253,23 +253,6 @@
                 "fields": ["atom:author or codemeta:author"],
             },
         ),
-        (
-            f"""\
-            <entry {XMLNS}>
-                <url>something</url>
-                <external_identifier>something-else</external_identifier>
-                <title>bar</title>
-                <author>someone</author>
-                <codemeta:datePublished>2020-aa-21</codemeta:datePublished>
-                <codemeta:dateCreated>2020-12-bb</codemeta:dateCreated>
-                {PROVENANCE_XML}
-            </entry>
-            """,
-            {
-                "summary": "Invalid date format",
-                "fields": ["codemeta:datePublished", "codemeta:dateCreated"],
-            },
-        ),
     ]
 ]
 
@@ -286,6 +269,29 @@
 _parameters3 = [
     (textwrap.dedent(metadata_ko), expected_summary)
     for (metadata_ko, expected_summary) in [
+        (
+            f"""\
+            <entry {XMLNS}>
+                <url>something</url>
+                <external_identifier>something-else</external_identifier>
+                <title>bar</title>
+                <author>someone</author>
+                <codemeta:datePublished>2020-aa-21</codemeta:datePublished>
+                <codemeta:dateCreated>2020-12-bb</codemeta:dateCreated>
+                {PROVENANCE_XML}
+            </entry>
+            """,
+            [
+                {
+                    "summary": ".*Reason: invalid value '2020-aa-21'.*",
+                    "fields": ["codemeta:datePublished"],
+                },
+                {
+                    "summary": ".*Reason: invalid value '2020-12-bb'.*",
+                    "fields": ["codemeta:dateCreated"],
+                },
+            ],
+        ),
         (
             f"""\
             <entry {XMLNS}>
@@ -297,30 +303,17 @@
                 <codemeta:dateCreated>2020-12-bb</codemeta:dateCreated>
             </entry>
             """,
-            {
-                "summary": "Invalid date format",
-                "fields": ["codemeta:datePublished", "codemeta:dateCreated"],
-            },
+            [
+                {
+                    "summary": ".*Reason: invalid value '2020-aa-21'.*",
+                    "fields": ["codemeta:datePublished"],
+                },
+                {
+                    "summary": ".*Reason: invalid value '2020-12-bb'.*",
+                    "fields": ["codemeta:dateCreated"],
+                },
+            ],
         ),
-    ]
-]
-
-
-@pytest.mark.parametrize("metadata_ko,expected_invalid_summary", _parameters3)
-def test_api_checks_check_metadata_fields_ko_and_missing_suggested_fields(
-    metadata_ko, expected_invalid_summary, swh_checks_deposit
-):
-    actual_check, error_detail = check_metadata(ElementTree.fromstring(metadata_ko))
-    assert actual_check is False
-    assert error_detail == {
-        "metadata": [expected_invalid_summary]
-        + [{"fields": [METADATA_PROVENANCE_KEY], "summary": SUGGESTED_FIELDS_MISSING,}]
-    }
-
-
-_parameters4 = [
-    (textwrap.dedent(metadata_ko), expected_summary)
-    for (metadata_ko, expected_summary) in [
         (
             f"""\
             <entry {XMLNS}>
@@ -335,13 +328,15 @@
                 </swh:deposit>
             </entry>
             """,
-            {
-                "summary": (
-                    r".*Reason: Unexpected child with tag 'swh:invalid'.*"
-                    r"Instance:.*swh:invalid.*"
-                ),
-                "fields": ["swh:deposit"],
-            },
+            [
+                {
+                    "summary": (
+                        r".*Reason: Unexpected child with tag 'swh:invalid'.*"
+                        r"Instance:.*swh:invalid.*"
+                    ),
+                    "fields": ["swh:deposit"],
+                }
+            ],
         ),
         (
             f"""\
@@ -360,12 +355,14 @@
                 </swh:deposit>
             </entry>
             """,
-            {
-                "summary": (
-                    r".*Reason: Unexpected child with tag 'swh:add_to_origin'.*"
-                ),
-                "fields": ["swh:deposit"],
-            },
+            [
+                {
+                    "summary": (
+                        r".*Reason: Unexpected child with tag 'swh:add_to_origin'.*"
+                    ),
+                    "fields": ["swh:deposit"],
+                }
+            ],
         ),
         (
             f"""\
@@ -384,14 +381,16 @@
                 </swh:deposit>
             </entry>
             """,
-            {
-                "summary": (
-                    r".*Reason: assertion test if false.*"
-                    r"Schema:\n*"
-                    r' *<xsd:assert[^>]+ id="swhdeposit-incompatible-create-and-add".*'
-                ),
-                "fields": ["swh:deposit"],
-            },
+            [
+                {
+                    "summary": (
+                        r".*Reason: assertion test if false.*"
+                        r"Schema:\n*"
+                        r' *<xsd:assert[^>]+ id="swhdeposit-incompatible-create-and-add".*'
+                    ),
+                    "fields": ["swh:deposit"],
+                }
+            ],
         ),
         (
             f"""\
@@ -410,14 +409,16 @@
                 </swh:deposit>
             </entry>
             """,
-            {
-                "summary": (
-                    r".*Reason: assertion test if false.*"
-                    r"Schema:\n*"
-                    r' *<xsd:assert[^>]+ id="swhdeposit-incompatible-create-and-reference".*'
-                ),
-                "fields": ["swh:deposit"],
-            },
+            [
+                {
+                    "summary": (
+                        r".*Reason: assertion test if false.*"
+                        r"Schema:\n*"
+                        r' *<xsd:assert[^>]+ id="swhdeposit-incompatible-create-and-reference".*'
+                    ),
+                    "fields": ["swh:deposit"],
+                }
+            ],
         ),
         (
             f"""\
@@ -436,14 +437,16 @@
                 </swh:deposit>
             </entry>
             """,
-            {
-                "summary": (
-                    r".*Reason: assertion test if false.*"
-                    r"Schema:\n*"
-                    r' *<xsd:assert[^>]+ id="swhdeposit-incompatible-add-and-reference".*'
-                ),
-                "fields": ["swh:deposit"],
-            },
+            [
+                {
+                    "summary": (
+                        r".*Reason: assertion test if false.*"
+                        r"Schema:\n*"
+                        r' *<xsd:assert[^>]+ id="swhdeposit-incompatible-add-and-reference".*'
+                    ),
+                    "fields": ["swh:deposit"],
+                }
+            ],
         ),
         (
             f"""\
@@ -460,10 +463,12 @@
                 </swh:deposit>
             </entry>
             """,
-            {
-                "summary": r".*Reason: Unexpected child with tag 'swh:origin'.*",
-                "fields": ["swh:deposit"],
-            },
+            [
+                {
+                    "summary": r".*Reason: Unexpected child with tag 'swh:origin'.*",
+                    "fields": ["swh:deposit"],
+                },
+            ],
         ),
         (
             f"""\
@@ -480,10 +485,12 @@
                 </swh:deposit>
             </entry>
             """,
-            {
-                "summary": r".*Reason: Unexpected child with tag 'swh:origin'.*",
-                "fields": ["swh:deposit"],
-            },
+            [
+                {
+                    "summary": r".*Reason: Unexpected child with tag 'swh:origin'.*",
+                    "fields": ["swh:deposit"],
+                },
+            ],
         ),
         (
             f"""\
@@ -500,25 +507,33 @@
                 </swh:deposit>
             </entry>
             """,
-            {
-                "summary": r".*Reason: Unexpected child with tag 'swh:object'.*",
-                "fields": ["swh:deposit"],
-            },
+            [
+                {
+                    "summary": r".*Reason: Unexpected child with tag 'swh:object'.*",
+                    "fields": ["swh:deposit"],
+                },
+            ],
         ),
     ]
 ]
 
 
-@pytest.mark.parametrize("metadata_ko,expected_summary", _parameters4)
+@pytest.mark.parametrize("metadata_ko,expected_summaries", _parameters3)
 def test_api_checks_check_metadata_ko_schema(
-    metadata_ko, expected_summary, swh_checks_deposit
+    metadata_ko, expected_summaries, swh_checks_deposit
 ):
     actual_check, error_detail = check_metadata(ElementTree.fromstring(metadata_ko))
     assert actual_check is False
-    assert len(error_detail["metadata"]) == 1, error_detail["metadata"]
-    assert error_detail["metadata"][0]["fields"] == expected_summary["fields"]
+    assert len(error_detail["metadata"]) == len(expected_summaries), error_detail[
+        "metadata"
+    ]
+
+    for (detail, expected_summary) in zip(error_detail["metadata"], expected_summaries):
+        assert detail["fields"] == expected_summary["fields"]
 
-    # xmlschema returns very detailed errors, we cannot reasonably test them
-    # for equality
-    summary = error_detail["metadata"][0]["summary"]
-    assert re.match(expected_summary["summary"], summary, re.DOTALL), summary
+        # xmlschema returns very detailed errors, we cannot reasonably test them
+        # for equality
+        summary = detail["summary"]
+        assert re.match(
+            expected_summary["summary"], summary, re.DOTALL
+        ), f"Failed to match {expected_summary['summary']!r} with:\n{summary}"
diff --git a/swh/deposit/xsd/codemeta.xsd b/swh/deposit/xsd/codemeta.xsd
new file mode 100644
--- /dev/null
+++ b/swh/deposit/xsd/codemeta.xsd
@@ -0,0 +1,16 @@
+<?xml version="1.0" encoding="utf-8"?>
+<xsd:schema xmlns:xsd="http://www.w3.org/2001/XMLSchema"
+            targetNamespace="https://doi.org/10.5063/SCHEMA/CODEMETA-2.0"
+            xmlns:codemeta="https://doi.org/10.5063/SCHEMA/CODEMETA-2.0"
+            elementFormDefault="qualified"
+            >
+  <!-- This is a non-exhaustive schema used to find likely errors in XML-encoded
+       Codemeta documents -->
+
+  <xsd:element name="datePublished" type="codemeta:DateOrDateTime" />
+  <xsd:element name="dateCreated" type="codemeta:DateOrDateTime" />
+
+  <xsd:simpleType name="DateOrDateTime">
+    <xsd:union memberTypes="xsd:date xsd:dateTime"/>
+  </xsd:simpleType>
+</xsd:schema>