First of all, TEMPEST shielding and EMP suppression are not exactly the same thing.

TEMPEST has to do with reducing radiation FROM equipment which could be intercepted by someone on the outside. Involves a lot of heavy shielding, broadband filtering/bypassing, etc.

EMP suppression is for the protection of your equipment. It can be achieved by LC filtering and fast-acting impulse suppressors like these:
http://www.polyphaser.com/kommerce_productdata.aspx?search_val=NEMP&x=0&y=0

Yes, utility power can be bypassed and filtered where it enters a faraday cage. It is done all the time in screen rooms used for RF equipment testing.