They may be looking for it; to leave information about the Apple Watch at
both businesses as a courtesy to the owner, if you turn it over to police, is
about the most you can do. The owner should be able to re-enable contact
with their watch, to maybe prove their ownership. Leave a trail of crumbs to
the police station so even hansel or grettel could find it.
It would be handy if there were a built-in way to message the owner from
the watch to their iphone; to suggest where the watch may be found. But
I doubt that idea be available right now. Chances are, the owner may have
used information such as the following link, to 'Mark as Missing' or unpair
the watch from their iphone.
Jun 6, 2016 - Turn on Mark as Missing from your paired iPhone: Open the Watch app on
your iPhone and tap the My Watch tab. Tap Apple Watch, then turn on Mark as Missing.
Confirm that you want to unpair and that you need to enter your Apple ID to pair your
Apple Watch again. If you forgot your Apple ID password, you can reset it.
various items indicate why - 'Find my iPhone' - won't help find a Watch:
https://www.google.com/#q=find+apple+watch+from+iphone
Being the watch is paired to the AppleID of the original registered owner, it amount to be
nearly worthless to anyone finding the item. ~ However that said, it should be easier for
the owner to locate a lost watch. As a cousin to the iPhone, it should just message him. 😝