diff --git a/django/test/testcases.py b/django/test/testcases.py
index 7b5c7cdd78..0e4d406464 100644
--- a/django/test/testcases.py
+++ b/django/test/testcases.py
@@ -477,11 +477,23 @@ class SimpleTestCase(unittest.TestCase):
 
         self.assertEqual(real_count, 0, msg_prefix + "Response should not contain %s" % text_repr)
 
+    def _check_test_client_response(self, response, attribute, method_name):
+        """
+        Raise a ValueError if the given response doesn't have the required
+        attribute.
+        """
+        if not hasattr(response, attribute):
+            raise ValueError(
+                f"{method_name}() is only usable on responses fetched using "
+                "the Django test Client."
+            )
+
     def assertFormError(self, response, form, field, errors, msg_prefix=''):
         """
         Assert that a form used to render the response has a specific field
         error.
         """
+        self._check_test_client_response(response, 'context', 'assertFormError')
         if msg_prefix:
             msg_prefix += ": "
 
@@ -543,6 +555,7 @@ class SimpleTestCase(unittest.TestCase):
         For non-form errors, specify ``form_index`` as None and the ``field``
         as None.
         """
+        self._check_test_client_response(response, 'context', 'assertFormsetError')
         # Add punctuation to msg_prefix
         if msg_prefix:
             msg_prefix += ": "
@@ -612,7 +625,7 @@ class SimpleTestCase(unittest.TestCase):
         if not found_formset:
             self.fail(msg_prefix + "The formset '%s' was not used to render the response" % formset)
 
-    def _assert_template_used(self, response, template_name, msg_prefix):
+    def _assert_template_used(self, response, template_name, msg_prefix, method_name):
 
         if response is None and template_name is None:
             raise TypeError('response and/or template_name argument must be provided')
@@ -620,11 +633,8 @@ class SimpleTestCase(unittest.TestCase):
         if msg_prefix:
             msg_prefix += ": "
 
-        if template_name is not None and response is not None and not hasattr(response, 'templates'):
-            raise ValueError(
-                "assertTemplateUsed() and assertTemplateNotUsed() are only "
-                "usable on responses fetched using the Django test Client."
-            )
+        if template_name is not None and response is not None:
+            self._check_test_client_response(response, 'templates', method_name)
 
         if not hasattr(response, 'templates') or (response is None and template_name):
             if response:
@@ -642,8 +652,8 @@ class SimpleTestCase(unittest.TestCase):
         the response. Also usable as context manager.
         """
         context_mgr_template, template_names, msg_prefix = self._assert_template_used(
-            response, template_name, msg_prefix)
-
+            response, template_name, msg_prefix, 'assertTemplateUsed',
+        )
         if context_mgr_template:
             # Use assertTemplateUsed as context manager.
             return _AssertTemplateUsedContext(self, context_mgr_template)
@@ -671,7 +681,7 @@ class SimpleTestCase(unittest.TestCase):
         rendering the response. Also usable as context manager.
         """
         context_mgr_template, template_names, msg_prefix = self._assert_template_used(
-            response, template_name, msg_prefix
+            response, template_name, msg_prefix, 'assertTemplateNotUsed',
         )
         if context_mgr_template:
             # Use assertTemplateNotUsed as context manager.
diff --git a/tests/test_utils/tests.py b/tests/test_utils/tests.py
index fbff188576..47ce93e2ca 100644
--- a/tests/test_utils/tests.py
+++ b/tests/test_utils/tests.py
@@ -558,14 +558,10 @@ class AssertTemplateUsedContextManagerTests(SimpleTestCase):
 
     def test_assert_used_on_http_response(self):
         response = HttpResponse()
-        error_msg = (
-            'assertTemplateUsed() and assertTemplateNotUsed() are only '
-            'usable on responses fetched using the Django test Client.'
-        )
-        with self.assertRaisesMessage(ValueError, error_msg):
+        msg = '%s() is only usable on responses fetched using the Django test Client.'
+        with self.assertRaisesMessage(ValueError, msg % 'assertTemplateUsed'):
             self.assertTemplateUsed(response, 'template.html')
-
-        with self.assertRaisesMessage(ValueError, error_msg):
+        with self.assertRaisesMessage(ValueError, msg % 'assertTemplateNotUsed'):
             self.assertTemplateNotUsed(response, 'template.html')
 
 
@@ -1288,6 +1284,15 @@ class TestFormset(formset_factory(TestForm)):
 
 
 class AssertFormErrorTests(SimpleTestCase):
+    def test_non_client_response(self):
+        msg = (
+            'assertFormError() is only usable on responses fetched using the '
+            'Django test Client.'
+        )
+        response = HttpResponse()
+        with self.assertRaisesMessage(ValueError, msg):
+            self.assertFormError(response, 'formset', 0, 'field', 'invalid value')
+
     def test_response_with_no_context(self):
         msg = 'Response did not use any contexts to render the response'
         response = mock.Mock(context=[])
@@ -1384,6 +1389,15 @@ class AssertFormsetErrorTests(SimpleTestCase):
             'form-0-field': field_value,
         }
 
+    def test_non_client_response(self):
+        msg = (
+            'assertFormsetError() is only usable on responses fetched using '
+            'the Django test Client.'
+        )
+        response = HttpResponse()
+        with self.assertRaisesMessage(ValueError, msg):
+            self.assertFormsetError(response, 'formset', 0, 'field', 'invalid value')
+
     def test_response_with_no_context(self):
         msg = 'Response did not use any contexts to render the response'
         response = mock.Mock(context=[])