If the electromagnetic bubble is just hovering over the city and only dipping in when required by a an electronic communication device..
then, by isolating your electronic devices, you can avoid being spotted. This view considers the big bubble to be the maternale superior, and all the smaller ones stretching towards her and trying to get her attention.
With mobile phones there is already the options of switching to airplane mode or swithcing it off altogether, but I believe this would open for a nice little putting-to-sleep ritual, (Sleeping Beauty in the crystal coffin) as a continuation of the already strong bonds we have to our phones. Other than the phone, there are a lot of electronic communicating devices in our homes that this could also apply to.