Could a suitably-reinforced faraday cage keep a smart weapon smart?

As labelled in the Ah, they’re 1920’s style “Death Rays”. thread: http://boards.straightdope.com/sdmb/showthread.php?threadid=202225

The topic came up that an atomic blast over a city would (in addition to destroying most or all of the city) disrupt all electronic communication and scramble all sorts of circuits, including making smart bombs stupid.

I also learned that a Faraday cage can block all manner of electro-magnetic noise, including radio waves…

With that said, if I had a cache of smart bombs in my underground bunker protected on the inside by a faraday cage, would my bombs still be “smart”?

Purely a hypothetical situation, of course.