Most of the faraday cages in military construction, while it does serve to protect from incoming RF disturbances such as an EMP and EMI, is actually primarily intended to protect from the outside listening in. Computers by nature emit a lot of RF signals that can actually be received, and even decoded by their patterns, thus possibly giving away top secret information. I did a job at an Air Force base just last year where I had to leave everything that could emit RF outside the control room we were in because of the possibility of receiving and recording signals from older analog equipment and technolgy, which was actually made easier by the faraday cage on the room. I got to see some pretty cool 'sniffers' that were permanently installed in the room to detect ANY RF emitting device that wasn't supposed to be there. I can't count the times folks forgot and walked in with their phones and set off the alarm. It was quite annoying, actually.
In most cases in modern hospitals, you'll also find their MRI, CT, and XRay equipment in rooms with Faraday cages in the walls and doors, and no windows. Those types of equipment ALL emit very nasty EMI and RFI that will create big problems for other electronic equipment in a hospital. Got a pacemaker? No MRI or CT for you without a lot of special procedures to prevent interfering with the device. I've had this explained to me several times in the past 5 years thanks to old cumulative injuries and a gradually increasing heart risk (Bradycardia) that made my cardiologist wave one in my face during my last appointment. Folks that are dependent on pacemakers are not going to fare well in an EMP of even low magnitude.
Your car, sort of IS a faraday cage, albeit, not a very well built one. Metal panels largely enclose all the things that make it work. Because it isn't completely enclosed (like a tank), though, most of the 'intelligent' modules are enclosed in metal boxes firmly grounded to the car's frame. That's just little Faraday cages in a bigger one, meaning the Department of Redundancy Department has already done their job. I don't think an EMP is going to have a significant impact on transportation. Considering the miles and miles of antennae in the electrical distribution system (transmission lines), yeah, I can see where that's going to be a problem. However, there's so much protective equipment in the electrical system, it would take several EMP's with very sophisticated targeting to first take out the control electronics, then the protective electronics, and finally actually create enough damage to the major equipment to delay more than a couple days' recovery to full operation. A couple days is a long time without Meta, though, for some.