diff --git a/lib/matplotlib/backends/qt_compat.py b/lib/matplotlib/backends/qt_compat.py
index 28650dc9ff83..e76ff67e1cef 100644
--- a/lib/matplotlib/backends/qt_compat.py
+++ b/lib/matplotlib/backends/qt_compat.py
@@ -133,7 +133,8 @@ def _isdeleted(obj):
     else:
         raise ImportError(
             "Failed to import any of the following Qt binding modules: {}"
-            .format(", ".join(_ETS.values())))
+            .format(", ".join([QT_API for _, QT_API in _candidates]))
+        )
 else:  # We should not get there.
     raise AssertionError(f"Unexpected QT_API: {QT_API}")
 _version_info = tuple(QtCore.QLibraryInfo.version().segments())
diff --git a/lib/matplotlib/tests/test_backends_interactive.py b/lib/matplotlib/tests/test_backends_interactive.py
index ade636433144..a8cbc8885daf 100644
--- a/lib/matplotlib/tests/test_backends_interactive.py
+++ b/lib/matplotlib/tests/test_backends_interactive.py
@@ -343,6 +343,26 @@ def test_qt5backends_uses_qt5():
     _run_helper(_implcore, timeout=_test_timeout)
 
 
+def _impl_missing():
+    import sys
+    # Simulate uninstalled
+    sys.modules["PyQt6"] = None
+    sys.modules["PyQt5"] = None
+    sys.modules["PySide2"] = None
+    sys.modules["PySide6"] = None
+
+    import matplotlib.pyplot as plt
+    with pytest.raises(ImportError, match="Failed to import any of the following Qt"):
+        plt.switch_backend("qtagg")
+    # Specifically ensure that Pyside6/Pyqt6 are not in the error message for qt5agg
+    with pytest.raises(ImportError, match="^(?:(?!(PySide6|PyQt6)).)*$"):
+        plt.switch_backend("qt5agg")
+
+
+def test_qt_missing():
+    _run_helper(_impl_missing, timeout=_test_timeout)
+
+
 def _impl_test_cross_Qt_imports():
     import sys
     import importlib