There are miniaturized advances in Faraday shielding which are amazing that I have seen at shows and tech expos. There are also devices out today both nuclear and non nuclear that can generate sufficient energy for either large or small scale EMP attacks. This is due to the new thrusts going into Asymmetric warfare.
Nuclear bursts in the stratosphere will also shower the place with protons. Those will collide with metal boxes, knocking electrons off the inside surfaces of the box. That secondary emission must be handled using a box inside a box.
EMP is a problem only if you are really close to the burst. For example, a 10KT ground burst causes EMP that can cause little damage when over 2 miles away. Big bombs make a higher density; however, I don't think they travel much farther than affects of the burst itself. High altitude burst with large warheads are more troublesome, but EMP from those things still follows the inverse square law. The military is concerned about all of this because the nukes will be aimed at their stuff. They want their electronics to survive a near miss.