Does Apple Watch give out a warning sound or vibration when it is out of range with your iPhone?

Hi

Apple Watch does not presently offer audible or haptic alerts if it is taken out of Bluetooth range of the paired iPhone. When the devices have become disconnected via Bluetooth, if the watch is also unable to connect to a known Wi-Fi network at that time, it will show the Disconnected icon at the top of the watch face:

However, you may find this third-party app helpful:

• Lookout – Security, Backup and Missing Device
  • "Shows you the distance between your iPhone and Apple Watch, and notifies you if they’re about to lose connection."
  • https://itunes.apple.com/us/app/lookout-security-backup-missing/id434893913?mt=8

If you would like to suggest that Apple considers adding Bluetooth disconnection alerts as a built-in feature, you can do so here:

https://www.apple.com/feedback/watch.html