diff --git a/starlette/middleware/errors.py b/starlette/middleware/errors.py
index f3de1629..4217185e 100644
--- a/starlette/middleware/errors.py
+++ b/starlette/middleware/errors.py
@@ -217,15 +217,15 @@ class ServerErrorMiddleware:
         traceback_obj = traceback.TracebackException.from_exception(
             exc, capture_locals=True
         )
-        frames = inspect.getinnerframes(
-            traceback_obj.exc_traceback, limit  # type: ignore
-        )
 
         exc_html = ""
         is_collapsed = False
-        for frame in reversed(frames):
-            exc_html += self.generate_frame_html(frame, is_collapsed)
-            is_collapsed = True
+        exc_traceback = exc.__traceback__
+        if exc_traceback is not None:
+            frames = inspect.getinnerframes(exc_traceback, limit)
+            for frame in reversed(frames):
+                exc_html += self.generate_frame_html(frame, is_collapsed)
+                is_collapsed = True
 
         # escape error class and text
         error = (
diff --git a/starlette/testclient.py b/starlette/testclient.py
index c17c5181..1d5e90dc 100644
--- a/starlette/testclient.py
+++ b/starlette/testclient.py
@@ -268,7 +268,6 @@ class WebSocketTestSession:
         self.app = app
         self.scope = scope
         self.accepted_subprotocol = None
-        self._loop = asyncio.new_event_loop()
         self._receive_queue = queue.Queue()  # type: queue.Queue
         self._send_queue = queue.Queue()  # type: queue.Queue
         self._thread = threading.Thread(target=self._run)
@@ -293,13 +292,16 @@ class WebSocketTestSession:
         """
         The sub-thread in which the websocket session runs.
         """
+        loop = asyncio.new_event_loop()
         scope = self.scope
         receive = self._asgi_receive
         send = self._asgi_send
         try:
-            self._loop.run_until_complete(self.app(scope, receive, send))
+            loop.run_until_complete(self.app(scope, receive, send))
         except BaseException as exc:
             self._send_queue.put(exc)
+        finally:
+            loop.close()
 
     async def _asgi_receive(self) -> Message:
         while self._receive_queue.empty():
diff --git a/tests/middleware/__init__.py b/tests/middleware/__init__.py
new file mode 100644
index 00000000..e69de29b