How to find your device with the serial number
How to find this device if it doesn’t show up on find my iPhone.
Apple Watch SE, watchOS 8
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You cannot track a lost or stolen device by its serial number. If it doesn't show in Find My, the only way to find it is the old fashioned, use your eyeballs, trace your steps kind of way.
See this link for help if you've lost your Apple Watch --> If your Apple Watch is lost or stolen - Apple Support