The accuracy of a "cheap" digital is generally much greater than a VERY expensive chronometer. Given the temperature variation, shock, etc., you'd be hard pressed to match the standalone accuracy of a digital watch.

The methods of calibrating time pieces can utilize a known position, and the observing the position of (various) celestial bodies -- sort-of reverse positioning where time is the variable.

You can then develop and "offset" from your existing timepiece.

Are you concerned with post aremegedon situation where radio broadcasts (not consumer local radio stations) would be interupted?

A digital watch often has a five-year battery (or so)