Electromagnetic radiation essentially works like an inductive cook top. It creates currents in metals and because the metals have resistance, they heat up. Little EMR like radio waves creates tiny currents, just big enough to amplify in to a sound signal, big EMR like an EMP will melt a high resistance Faraday cage and fry the electronics inside.
In my opinion mechanical locks are more reliable and any electronic lock with a backup key is only as good as the key lock (way less secure than a good combination lock).
On the other hand, I think the lock is only a small part of real security and you should make it hard for a theif to even get to the lock.
If you want to prepare against EMP, you need spare electronics that you can keep locked inside a serious Faraday cage, well grounded with small gaps on the door and probably solid metal construction rather than mesh. I don't think I need a safe for this, probably just a modified jobs site toolbox with a good puck style lock. All I need are some batteries, radios, probably a computer with a lot of valuable information and books stored on it, solar panels and a charge controller.