This has concerned me quite a bit for a long time, what with society's increasing reliance on electronic data storage.
I work in healthcare, and the idea of everybody in a city losing their entire medical history, and for patients in a hospital losing their ongoing care histories as well as x-rays is not a scenario that I look forward to. A few EMP detonations will bring us all down to a Medieval level pretty darned fast
The upper echelons of the military have diamond substrate CPUs. Those will laugh at an EMP.
Shielding techniques can be pretty effective too. A grounded metal building that never lets you get a cellphone signal may ground an EMP as well.
Optical CD storage will be okay.