Faraday Cages

[Legbreaker]

However, wiring is usually throughout the vehicle and would act like an antenna, channelling the EMP waves right into the heart of things...
Yes, wiring is insulated, but not against EMP.

How long is an EMP wavelength?
Well, it appears to actually vary over a very wide range. While close mesh will help, it's not going to stop everything. The most common advice I've found is to make sure all holes are closed ie use solid sheeting in preference to anything else otherwise you're running a significant risk of at least partial EMP exposure (which if you're at 40,000 feet could be just enough to really ruin your day).

The quote below (from wiki) I think is rather telling.

Misconception:Nuclear EMP is not a problem because there are ways to protect against it.
The fact: Although there are ways to protect against nuclear EMP (or to quickly begin repairs where protection is not practical), the United States EMP Commission determined that such protections are almost completely absent in the civilian infrastructure of the United States, and that even large sectors of the United States military services were no longer protected against EMP to the level that they were during the Cold War.