diff --git a/swh/core/api/__init__.py b/swh/core/api/__init__.py
--- a/swh/core/api/__init__.py
+++ b/swh/core/api/__init__.py
@@ -1,4 +1,4 @@
-# Copyright (C) 2015-2020  The Software Heritage developers
+# Copyright (C) 2015-2022  The Software Heritage developers
 # See the AUTHORS file at the top-level directory of this distribution
 # License: GNU General Public License version 3, or any later version
 # See top-level LICENSE file for more information
@@ -320,9 +320,6 @@
         status_code = response.status_code
         status_class = response.status_code // 100
 
-        if status_code == 404:
-            raise RemoteException(payload="404 not found", response=response)
-
         exception = None
 
         # TODO: only old servers send pickled error; stop trying to unpickle
@@ -356,6 +353,9 @@
         except (TypeError, pickle.UnpicklingError):
             raise RemoteException(payload=data, response=response)
 
+        if status_code == 404 and type(exception) not in self.reraise_exceptions:
+            raise RemoteException(payload="404 not found", response=response)
+
         if exception:
             raise exception from None
 
diff --git a/swh/core/api/tests/test_rpc_client_server.py b/swh/core/api/tests/test_rpc_client_server.py
--- a/swh/core/api/tests/test_rpc_client_server.py
+++ b/swh/core/api/tests/test_rpc_client_server.py
@@ -1,4 +1,4 @@
-# Copyright (C) 2018-2019  The Software Heritage developers
+# Copyright (C) 2018-2022  The Software Heritage developers
 # See the AUTHORS file at the top-level directory of this distribution
 # License: GNU General Public License version 3, or any later version
 # See top-level LICENSE file for more information
@@ -19,6 +19,10 @@
     """Another exception class to distinguish error handlers"""
 
 
+class NotFoundException(Exception):
+    pass
+
+
 # this class is used on the server part
 class RPCTest:
     @remote_api_endpoint("endpoint_url")
@@ -42,6 +46,10 @@
     def raise_expectedexc(self):
         raise ExpectedException("that was expected")
 
+    @remote_api_endpoint("raises_not_found_exc")
+    def raise_not_found_exc(self):
+        raise NotFoundException()
+
 
 # this class is used on the client part. We cannot inherit from RPCTest
 # because the automagic metaclass based code that generates the RPCClient
@@ -70,9 +78,14 @@
     def raise_expectedexc(self):
         return "nothing"
 
+    @remote_api_endpoint("raises_not_found_exc")
+    def raise_not_found_exc(self):
+        return "not found"
+
 
 class RPCTestClient(RPCClient):
     backend_class = RPCTest2
+    reraise_exceptions = [NotFoundException]
 
 
 @pytest.fixture
@@ -85,6 +98,10 @@
     def my_expected_error_handler(exception):
         return error_handler(exception, encode_data_server, status_code=400)
 
+    @application.errorhandler(NotFoundException)
+    def not_found_error_handler(exception):
+        return error_handler(exception, encode_data_server, status_code=404)
+
     @application.errorhandler(Exception)
     def my_error_handler(exception):
         return error_handler(exception, encode_data_server)
@@ -111,6 +128,13 @@
         swh_rpc_client.not_on_server()
 
 
+def test_api_reraise_not_found(swh_rpc_client):
+    # A 'missing' endpoint (server-side) should raise an exception
+    # due to a 404, since at the end, we do a GET/POST an inexistent URL
+    with pytest.raises(NotFoundException):
+        swh_rpc_client.raise_not_found_exc()
+
+
 def test_api_endpoint_kwargs(swh_rpc_client):
     res = swh_rpc_client.something(data="whatever")
     assert res == "whatever"