diff --git a/tests/local_testing/test_custom_callback_input.py b/tests/local_testing/test_custom_callback_input.py
index 545039e60ba..04d83a09ffb 100644
--- a/tests/local_testing/test_custom_callback_input.py
+++ b/tests/local_testing/test_custom_callback_input.py
@@ -1134,8 +1134,12 @@ def test_standard_logging_payload_audio(turn_off_message_logging, stream):
                 stream=stream,
             )
         except Exception as e:
-            if "openai-internal" in str(e):
+            err = str(e)
+            if "openai-internal" in err:
                 pytest.skip("Skipping test due to openai-internal error")
+            if "model_not_found" in err or "does not exist" in err:
+                pytest.skip(f"Skipping test - upstream model unavailable: {err}")
+            raise
 
         if stream:
             for chunk in response:
diff --git a/tests/local_testing/test_stream_chunk_builder.py b/tests/local_testing/test_stream_chunk_builder.py
index 24fdf49c16c..cf61f8b8777 100644
--- a/tests/local_testing/test_stream_chunk_builder.py
+++ b/tests/local_testing/test_stream_chunk_builder.py
@@ -657,8 +657,12 @@ def test_stream_chunk_builder_openai_audio_output_usage():
             stream_options={"include_usage": True},
         )
     except Exception as e:
-        if "openai-internal" in str(e):
+        err = str(e)
+        if "openai-internal" in err:
             pytest.skip("Skipping test due to openai-internal error")
+        if "model_not_found" in err or "does not exist" in err:
+            pytest.skip(f"Skipping test - upstream model unavailable: {err}")
+        raise
 
     chunks = []
     for chunk in completion: