diff --git a/tailcat.go b/tailcat.go
index a0eba13c4..f7d6085ef 100644
--- a/tailcat.go
+++ b/tailcat.go
@@ -297,6 +297,8 @@ type Server struct {
 
 	lb *locoBackend // non-nil once Start has been called
 
+	closeOnce sync.Once
+
 	// AllowProxy, if non-nil, reports whether
 	// a TCP or UDP proxy is allowed for that target.
 	AllowProxy func(netip.AddrPort) bool
@@ -519,7 +521,11 @@ func (s *Server) Close() error {
 	if s.lb == nil {
 		return nil // never started
 	}
-	return s.lb.Close()
+	var err error
+	s.closeOnce.Do(func() {
+		err = s.lb.Close()
+	})
+	return err
 }
 
 // DrainTCP waits until every TCP connection in the server's netstack
@@ -1411,6 +1417,8 @@ type Client struct {
 	key     key.NodePrivate // the effective node identity; Key or generated
 	started bool
 
+	closeOnce sync.Once
+
 	upDone atomic.Bool // whether the server has meowed us at least once
 }
 
@@ -1552,7 +1560,11 @@ func (c *Client) Close() error {
 	if c.lb == nil {
 		return nil // never used
 	}
-	return c.lb.Close()
+	var err error
+	c.closeOnce.Do(func() {
+		err = c.lb.Close()
+	})
+	return err
 }
 
 // PingResult is the result of a successful [Client.Ping] call.
diff --git a/tailcat_test.go b/tailcat_test.go
index f6089a855..786fd6d24 100644
--- a/tailcat_test.go
+++ b/tailcat_test.go
@@ -381,3 +381,37 @@ func TestFetchDERPMapMemoryCache(t *testing.T) {
 		t.Errorf("fetches = %d; want 1", n)
 	}
 }
+
+// TestDoubleClose verifies that calling Close more than once on a
+// [Server] or [Client] is harmless and does not panic or error.
+func TestDoubleClose(t *testing.T) {
+	t.Parallel()
+
+	dm := integration.RunDERPAndSTUN(t, mkLogger(t, "derpstun"), "127.0.0.1")
+	reg := dm.Regions[1]
+	if reg == nil {
+		t.Fatal("no region 1 in derpmap")
+	}
+
+	s := &Server{Logf: mkLogger(t, "server"), Region: reg}
+	if err := s.Start(); err != nil {
+		t.Fatalf("server Start: %v", err)
+	}
+
+	c := &Client{Server: s.ConnBlob(), Logf: mkLogger(t, "client")}
+	PingForTest(t, s, c)
+
+	if err := c.Close(); err != nil {
+		t.Fatalf("first client Close: %v", err)
+	}
+	if err := c.Close(); err != nil {
+		t.Fatalf("second client Close: %v", err)
+	}
+
+	if err := s.Close(); err != nil {
+		t.Fatalf("first server Close: %v", err)
+	}
+	if err := s.Close(); err != nil {
+		t.Fatalf("second server Close: %v", err)
+	}
+}