Nuclear weapons have a double flash signature, and we have sattelites designed to pick them out.

They also are traceable, the nuclear material retains it's trace elements in its fallout form.

Even small devices like the infamous artillery fired Davey Crockett tactical nuke let off potentially fatal radiation for a quarter mile. Also the film's would have suffer some sort of gamma radiation, not an EMP neccesarily, but noticeable. Best case scenario, munitions/rocket fuel stored horribly. Worst case? Hezbollah rocket/bomb factory taken out by ((them)). Big ol blast, though.