Stolen Apple Watch

All you can do now is put it in Lost Mode in case someone finds and charges it. See the 'Put your Apple Watch in Lost Mode' section in:

If your Apple Watch is lost or stolen - Apple Support

If the battery is dead, the only way to find it is by using your eyeballs to find it. Sorry. Do make sure to follow the advice in the Related Article Link at the top of the page, which brought you here.