diff --git a/chess/pgn.py b/chess/pgn.py
index 3d4d7e5ff..6a1abea06 100644
--- a/chess/pgn.py
+++ b/chess/pgn.py
@@ -566,7 +566,8 @@ def set_clock(self, seconds: Optional[float]) -> None:
         """
         clk = ""
         if seconds is not None:
-            seconds = max(0, seconds)
+            # nearest ms, otherwise 59.9996 becomes an invalid :60
+            seconds = round(max(0, seconds), 3)
             hours = int(seconds // 3600)
             minutes = int(seconds % 3600 // 60)
             seconds = seconds % 3600 % 60
@@ -595,7 +596,8 @@ def set_emt(self, seconds: Optional[float]) -> None:
         """
         emt = ""
         if seconds is not None:
-            seconds = max(0, seconds)
+            # nearest ms, otherwise 59.9996 becomes an invalid :60
+            seconds = round(max(0, seconds), 3)
             hours = int(seconds // 3600)
             minutes = int(seconds % 3600 // 60)
             seconds = seconds % 3600 % 60
diff --git a/test.py b/test.py
index a481c2adb..1f2de2ac9 100755
--- a/test.py
+++ b/test.py
@@ -2970,6 +2970,14 @@ def test_float_emt(self):
         self.assertEqual(game.comments, ["[%emt 0:00:00]"])  # Clamped
         self.assertEqual(game.emt(), 0)
 
+        game.set_emt(59.9996)
+        self.assertEqual(game.comments, ["[%emt 0:01:00]"])
+        self.assertEqual(game.emt(), 60)
+
+        game.set_emt(3599.9999)
+        self.assertEqual(game.comments, ["[%emt 1:00:00]"])
+        self.assertEqual(game.emt(), 3600)
+
     def test_float_clk(self):
         game = chess.pgn.Game()
         game.comments = ["[%clk 0:00:01.234]"]
@@ -2983,6 +2991,14 @@ def test_float_clk(self):
         self.assertEqual(game.comments, ["[%clk 0:00:00]"])  # Clamped
         self.assertEqual(game.clock(), 0)
 
+        game.set_clock(59.9996)
+        self.assertEqual(game.comments, ["[%clk 0:01:00]"])
+        self.assertEqual(game.clock(), 60)
+
+        game.set_clock(3599.9999)
+        self.assertEqual(game.comments, ["[%clk 1:00:00]"])
+        self.assertEqual(game.clock(), 3600)
+
     def test_node_turn(self):
         game = chess.pgn.Game()
         self.assertEqual(game.turn(), chess.WHITE)