diff --git a/swh/model/tests/test_identifiers.py b/swh/model/tests/test_identifiers.py
--- a/swh/model/tests/test_identifiers.py
+++ b/swh/model/tests/test_identifiers.py
@@ -927,37 +927,6 @@
                 },
             )
 
-    def test_parse_swhid_parsing_error(self):
-        for swhid in [
-            ("swh:1:cnt"),
-            ("swh:1:"),
-            ("swh:"),
-            ("swh:1:cnt:"),
-            ("foo:1:cnt:abc8bc9d7a6bcf6db04f476d29314f157507d505"),
-            ("swh:2:dir:def8bc9d7a6bcf6db04f476d29314f157507d505"),
-            ("swh:1:foo:fed8bc9d7a6bcf6db04f476d29314f157507d505"),
-            ("swh:1:dir:0b6959356d30f1a4e9b7f6bca59b9a336464c03d;invalid;" "malformed"),
-            ("swh:1:snp:gh6959356d30f1a4e9b7f6bca59b9a336464c03d"),
-            ("swh:1:snp:foo"),
-        ]:
-            with self.assertRaises(ValidationError):
-                identifiers.parse_swhid(swhid)
-
-    def test_persistentid_class_validation_error(self):
-        for _ns, _version, _type, _id in [
-            ("foo", 1, CONTENT, "abc8bc9d7a6bcf6db04f476d29314f157507d505"),
-            ("swh", 2, DIRECTORY, "def8bc9d7a6bcf6db04f476d29314f157507d505"),
-            ("swh", 1, "foo", "fed8bc9d7a6bcf6db04f476d29314f157507d505"),
-            ("swh", 1, SNAPSHOT, "gh6959356d30f1a4e9b7f6bca59b9a336464c03d"),
-        ]:
-            with self.assertRaises(ValidationError):
-                SWHID(
-                    namespace=_ns,
-                    scheme_version=_version,
-                    object_type=_type,
-                    object_id=_id,
-                )
-
 
 class OriginIdentifier(unittest.TestCase):
     def setUp(self):
@@ -1077,6 +1046,78 @@
         normalize_timestamp(dict_input)
 
 
+@pytest.mark.parametrize(
+    "swhid,expected_error",
+    [
+        ("swh:1:cnt", "Wrong format: There should be 4 mandatory values"),
+        ("swh:1:", "Wrong format: There should be 4 mandatory values"),
+        ("swh:", "Wrong format: There should be 4 mandatory values"),
+        ("swh:1:cnt:", "Wrong format: Identifier should be present"),
+        (
+            "foo:1:cnt:abc8bc9d7a6bcf6db04f476d29314f157507d505",
+            "Wrong format: only supported namespace is 'swh'",
+        ),
+        (
+            "swh:2:dir:def8bc9d7a6bcf6db04f476d29314f157507d505",
+            "Wrong format: only supported version is 1",
+        ),
+        (
+            "swh:1:foo:fed8bc9d7a6bcf6db04f476d29314f157507d505",
+            "Wrong input: Supported types are",
+        ),
+        (
+            "swh:1:dir:0b6959356d30f1a4e9b7f6bca59b9a336464c03d;invalid;malformed",
+            "Contextual data is badly formatted, form key=val expected",
+        ),
+        ("swh:1:snp:gh6959356d30f1a4e9b7f6bca59b9a336464c03d", "Unexpected characters"),
+        ("swh:1:snp:foo", "Unexpected characters"),
+    ],
+)
+def test_parse_swhid_parsing_error(swhid, expected_error):
+    with pytest.raises(ValidationError, match=expected_error):
+        identifiers.parse_swhid(swhid)
+
+
+@pytest.mark.parametrize(
+    "ns,version,type,id,expected_error",
+    [
+        (
+            "foo",
+            1,
+            CONTENT,
+            "abc8bc9d7a6bcf6db04f476d29314f157507d505",
+            "Wrong format: only supported namespace is 'swh'",
+        ),
+        (
+            "swh",
+            2,
+            DIRECTORY,
+            "def8bc9d7a6bcf6db04f476d29314f157507d505",
+            "Wrong format: only supported version is 1",
+        ),
+        (
+            "swh",
+            1,
+            "foo",
+            "fed8bc9d7a6bcf6db04f476d29314f157507d505",
+            "Wrong input: Supported types are",
+        ),
+        (
+            "swh",
+            1,
+            SNAPSHOT,
+            "gh6959356d30f1a4e9b7f6bca59b9a336464c03d",
+            "Unexpected characters",
+        ),
+    ],
+)
+def test_SWHID_class_validation_error(ns, version, type, id, expected_error):
+    with pytest.raises(ValidationError, match=expected_error):
+        SWHID(
+            namespace=ns, scheme_version=version, object_type=type, object_id=id,
+        )
+
+
 def test_swhid_hash():
     object_id = "94a9ed024d3859793618152ea559a168bbcbb5e2"