It creates a massive electromagnetic field that induces huge voltages across conductors. (Remember that this is basically how generators work. They move physical magnets that induce electricity in coils of wires. The e-bombs replace the magnets with a microwave pulse, and it only happens once instead of continuously.) It should basically fry any electronic system, as they're generally not going to have the capacity to deal with kilovolt or megavolt sized EMFs.

They say that the effective range is fairly small and nearly impossible to direct, though.

technical paper on e-bombs