Interference of that kind is easy to detect. Move the clock really up close and around the compass until you see the needle move so it points straight at the clock (or away from it). Then increase the distance but not the angle between the clock and the compass. Watch the needle point north again.


Usually, the distance required for your watch to influence your compass is too small for having any practical consequences. But it is good routine to actually CHECK this. In some cases (such as holding the compass in your left hand with a heavy watch) you may actually influence the accuracy. But this is easy to fix (such as moving the compass to your right hand).


I've been to high arctic where the magnetic field lines are close to vertical - which also means that the horizontal magnetic component is very small. Up there it doesn't take much to influence your compass. Standard procedure for having reliable compass readings was to remove any guns and step away from snowmobiles.