You raise a valid concern that I hope I can put to rest, at least in terms of military systems. The military has been aware of EMP effects on their systems for a long time. The Air Force has a massive wooden structure at Kirkland AFB, NM where aircraft are tested for EMP vulnerability. Here's a picture of the structure holding a B-52 bomber that's being tested. Shielding can be incorporated into a canopy either by very fine wires or by very thin coatings. As you might imagine, many of the details for such protection are probably classified to avoid exposing the capabilities and vulnerabilities. Suffice it to say that military weapons systems were designed to survive EMP and are tested for vulnerability.

The real danger of E-bombs is the damage they could do to non-hardened civilian systems. You could do more damage to an economy with a couple E-bombs than you did with nukes. If you fry electrical substations, computer systems, communications switching centers, heart pacemakers, and most other non-hardened electronics including that in cars and perhaps some civilian airliners, well, you could cost billions in losses in very short order. For example, an e-bomb detonated near Wall Street could well fry most of the electronics in the stock market trading houses. On an average day, over a billion shares of stock are traded on the NYSE alone, so it isn't hard to imagine what a few weeks of downtime would cost in economic activity.