Electro Magnetic Pulse and is created by a nuclear blast. Donn already covered that. What he didn't cover is what it really does.
First, in order to generate an EMP large enough to do the damage suggested, you need a nuclear blast. That's pretty unlikely. Second, an EMP has a limited range. The further you are from the blast, the less likely the EMP will damage any component you have.
So, to be truly concerned about an EMP, you must first be in a place where it is likely a nuclear weapon will be detonated (altitude is irrelevant by the way), then someone actually has to set one off.
Modern electronics are more susceptible than stuff from say the '60s. Still, if you're 50 miles from ground zero, it's unlikely any of your electronics will be damaged. If you're within 50 miles of a nuclear blast, you have bigger problems than a working watch.
Not arguing here, but how do you determine that a watch has lost a second in a month?
If I had time to do that calculation, the lost second wouldn't matter...
GPS is a wonderful thing.
In order to have really precise navigation, you need quality time. Thus, the GPS system is tied to the atomic clock at NIST in Boulder, Colorado. The short version is, your cell phone is tied to the GPS system and pretty much dead nuts on. So, check your watch against your cell phone and you're as close as you're gonna get.