diff --git a/django/db/backends/base/operations.py b/django/db/backends/base/operations.py
index 4e6a67685f..12f37e3404 100644
--- a/django/db/backends/base/operations.py
+++ b/django/db/backends/base/operations.py
@@ -754,6 +754,10 @@ class BaseDatabaseOperations:
                 msg = "%s is not a recognized format." % normalized_format
                 if supported_formats:
                     msg += " Allowed formats: %s" % ", ".join(sorted(supported_formats))
+                else:
+                    msg += (
+                        f" {self.connection.display_name} does not support any formats."
+                    )
                 raise ValueError(msg)
         if options:
             raise ValueError("Unknown options: %s" % ", ".join(sorted(options.keys())))
diff --git a/tests/queries/test_explain.py b/tests/queries/test_explain.py
index 1d17ef8191..f61fe01e9d 100644
--- a/tests/queries/test_explain.py
+++ b/tests/queries/test_explain.py
@@ -74,6 +74,8 @@ class ExplainTests(TestCase):
             msg += " Allowed formats: %s" % ", ".join(
                 sorted(connection.features.supported_explain_formats)
             )
+        else:
+            msg += f" {connection.display_name} does not support any formats."
         with self.assertRaisesMessage(ValueError, msg):
             Tag.objects.explain(format="does not exist")