A modern warship can be disabled by an electro magnetic pulse? There is shielding against such radiation. Can an EMP weapon pass through a wall of lead? Do US destroyers not have such shielding? And do they not have redundancy? Systems which can take over from damaged systems?
EMP's can potentially be of different strengths. They are also rather difficult to generate, so while designs can be made to shield against them (and indeed, military systems are hardened to a degree) much is going to depend on where the EMP occurred, and of what strength/intensity.
Also the term 'mission-kill' exists for a reason. Redundancy does tend to exist in military platforms, to a degree that is feasible and practical. Using an
Arleigh Burke-class DDG as an example, they tend to mount four SPY-1 panels, one each facing forward, aft, port and starboard. Rendering any of the panels inoperative would likely result in a 'mission-kill' since any least one quarter of the ship's facing is now effectively blind. Or alternately, if the magnetron(s) which is used to generate the signals transmitted by the panels fails, then the whole system basically fails.
Also worth noting, in the event of a damaging EA or EMP, multiple systems are likely going to be impacted, since shielding external arrays is basically ineffective/impossible. In order for most of the various electronic sensors and communications systems to be functional, at least part of them need to be exposed so they can emit or receive signals. In order to shield or harden something vs. EMP, then either material is needed to block the EMP, or ground out/redirect the pulse. Unfortunately, for something like a radio aerial which needs to be able to send and receive signals, if it is shielded from an EMP, then it is also shielded from the RF radiation needed to receive a radio signal. By extension, it would also be contained in such a way that any RF radiation the aerial would be trying to send out would also be contained.
Now EMP and EA, and some of the related direct energy technology is not the end-all, be-all since they are difficult to create and especially weaponize, but they absolutely have potential. Particularly since they can be used to degrade much of the technology which a force can use to enhance it's capabilities.