Annette Taylor has sent me this link. Rather than turning off a high-voltage power line when you work on it, you just wear one of these special anti-electricity suits.
Of course, there’s nothing hi-tech about them (at least, not conceptually). If you put one of these on, you are in your personal Faraday Cage, and the electric field inside will be zero. Another way of thinking about it is that any electrical current will travel along the suit, not into you, so you are protected.
It would be fun to try one out, I reckon.
12 July 2011: Annette has advised me I’ve got the wrong link there. Try this one: http://www.number8network.co.nz/2011/07/03/471/