diff --git a/mypy/dmypy/client.py b/mypy/dmypy/client.py
index efa1b5f01288..ee786fdd7436 100644
--- a/mypy/dmypy/client.py
+++ b/mypy/dmypy/client.py
@@ -665,10 +665,15 @@ def request(
         return {"error": str(err)}
     # TODO: Other errors, e.g. ValueError, UnicodeError
     else:
-        # Display debugging output written to stdout in the server process for convenience.
+        # Display debugging output written to stdout/stderr in the server process for convenience.
         stdout = response.get("stdout")
         if stdout:
             sys.stdout.write(stdout)
+        stderr = response.get("stderr")
+        if stderr:
+            print("-" * 79)
+            print("stderr:")
+            sys.stdout.write(stderr)
         return response
 
 
diff --git a/mypy/dmypy_server.py b/mypy/dmypy_server.py
index 7227cd559946..3cc50f4ece36 100644
--- a/mypy/dmypy_server.py
+++ b/mypy/dmypy_server.py
@@ -215,7 +215,9 @@ def serve(self) -> None:
                 with server:
                     data = receive(server)
                     debug_stdout = io.StringIO()
+                    debug_stderr = io.StringIO()
                     sys.stdout = debug_stdout
+                    sys.stderr = debug_stderr
                     resp: dict[str, Any] = {}
                     if "command" not in data:
                         resp = {"error": "No command found in request"}
@@ -233,9 +235,11 @@ def serve(self) -> None:
                                 resp = {"error": "Daemon crashed!\n" + "".join(tb)}
                                 resp.update(self._response_metadata())
                                 resp["stdout"] = debug_stdout.getvalue()
+                                resp["stderr"] = debug_stderr.getvalue()
                                 server.write(json.dumps(resp).encode("utf8"))
                                 raise
                     resp["stdout"] = debug_stdout.getvalue()
+                    resp["stderr"] = debug_stderr.getvalue()
                     try:
                         resp.update(self._response_metadata())
                         server.write(json.dumps(resp).encode("utf8"))