diff --git a/lib/matplotlib/backends/backend_gtk3.py b/lib/matplotlib/backends/backend_gtk3.py
index 1f9408b0668a..2f34248837dc 100644
--- a/lib/matplotlib/backends/backend_gtk3.py
+++ b/lib/matplotlib/backends/backend_gtk3.py
@@ -367,6 +367,7 @@ def add_widget(child):
 
         self.window.set_default_size(w, h)
 
+        self._destroying = False
         self.window.connect("destroy", lambda *args: Gcf.destroy(self))
         self.window.connect("delete_event", lambda *args: Gcf.destroy(self))
         if mpl.is_interactive():
@@ -376,6 +377,13 @@ def add_widget(child):
         self.canvas.grab_focus()
 
     def destroy(self, *args):
+        if self._destroying:
+            # Otherwise, this can be called twice when the user presses 'q',
+            # which calls Gcf.destroy(self), then this destroy(), then triggers
+            # Gcf.destroy(self) once again via
+            # `connect("destroy", lambda *args: Gcf.destroy(self))`.
+            return
+        self._destroying = True
         self.vbox.destroy()
         self.window.destroy()
         self.canvas.destroy()
diff --git a/lib/matplotlib/backends/backend_wx.py b/lib/matplotlib/backends/backend_wx.py
index 7adc47e0de16..b8b6034d11bd 100644
--- a/lib/matplotlib/backends/backend_wx.py
+++ b/lib/matplotlib/backends/backend_wx.py
@@ -1008,7 +1008,8 @@ def _onClose(self, event):
         self.canvas.close_event()
         self.canvas.stop_event_loop()
         Gcf.destroy(self)
-        # self.Destroy()
+        if self:
+            self.Destroy()
 
     def GetToolBar(self):
         """Override wxFrame::GetToolBar as we don't have managed toolbar"""
@@ -1066,7 +1067,7 @@ def show(self):
 
     def destroy(self, *args):
         _log.debug("%s - destroy()", type(self))
-        self.frame.Destroy()
+        self.frame.Close()
         wxapp = wx.GetApp()
         if wxapp:
             wxapp.Yield()
diff --git a/lib/matplotlib/tests/test_backends_interactive.py b/lib/matplotlib/tests/test_backends_interactive.py
index e53aa646484d..af8cbd2febf4 100644
--- a/lib/matplotlib/tests/test_backends_interactive.py
+++ b/lib/matplotlib/tests/test_backends_interactive.py
@@ -111,6 +111,7 @@ def check_alt_backend(alt_backend):
 timer.add_callback(FigureCanvasBase.key_press_event, fig.canvas, "q")
 # Trigger quitting upon draw.
 fig.canvas.mpl_connect("draw_event", lambda event: timer.start())
+fig.canvas.mpl_connect("close_event", print)
 
 plt.show()
 """
@@ -120,12 +121,14 @@ def check_alt_backend(alt_backend):
 @pytest.mark.parametrize("backend", _get_testable_interactive_backends())
 @pytest.mark.flaky(reruns=3)
 def test_interactive_backend(backend):
-    proc = subprocess.run([sys.executable, "-c", _test_script],
-                          env={**os.environ, "MPLBACKEND": backend},
-                          timeout=_test_timeout)
+    proc = subprocess.run(
+        [sys.executable, "-c", _test_script],
+        env={**os.environ, "MPLBACKEND": backend}, timeout=_test_timeout,
+        stdout=subprocess.PIPE, universal_newlines=True)
     if proc.returncode:
         pytest.fail("The subprocess returned with non-zero exit status "
                     f"{proc.returncode}.")
+    assert proc.stdout.count("CloseEvent") == 1
 
 
 @pytest.mark.skipif('SYSTEM_TEAMFOUNDATIONCOLLECTIONURI' in os.environ,