diff --git a/tokio/src/time/driver/mod.rs b/tokio/src/time/driver/mod.rs
index cf2290bc3b9..99718774793 100644
--- a/tokio/src/time/driver/mod.rs
+++ b/tokio/src/time/driver/mod.rs
@@ -129,7 +129,7 @@ impl ClockTime {
             .unwrap_or_else(|| Duration::from_secs(0));
         let ms = dur.as_millis();
 
-        ms.try_into().expect("Duration too far into the future")
+        ms.try_into().unwrap_or(u64::MAX)
     }
 
     pub(self) fn tick_to_duration(&self, t: u64) -> Duration {
diff --git a/tokio/tests/time_sleep.rs b/tokio/tests/time_sleep.rs
index 20477d26bb7..97cadecb0a5 100644
--- a/tokio/tests/time_sleep.rs
+++ b/tokio/tests/time_sleep.rs
@@ -235,22 +235,6 @@ async fn long_sleeps() {
     assert!(tokio::time::Instant::now() <= deadline + Duration::from_millis(1));
 }
 
-#[tokio::test]
-#[should_panic(expected = "Duration too far into the future")]
-async fn very_long_sleeps() {
-    tokio::time::pause();
-
-    // Some platforms (eg macos) can't represent times this far in the future
-    if let Some(deadline) = tokio::time::Instant::now().checked_add(Duration::from_secs(1u64 << 62))
-    {
-        tokio::time::sleep_until(deadline).await;
-    } else {
-        // make it pass anyway (we can't skip/ignore the test based on the
-        // result of checked_add)
-        panic!("Duration too far into the future (test ignored)")
-    }
-}
-
 #[tokio::test]
 async fn reset_after_firing() {
     let timer = tokio::time::sleep(std::time::Duration::from_millis(1));