If the hill is steep enough, I get really aero and stop pedaling. I read somewhere that above about 25 mph, you are better off coasting in a tucked position from an energy standpoint. The legs flailing around in circles make pretty much drag at those speeds. Of course an exception is if you are racing and need to maintain higher speeds. I seldom allow myself to go much over 30 mph anymore. I've had a few speed wobble issues in the past and they are scary!
I usually shift to a higher gear in anticipation of pedaling again. Once my cadence starts to fall, I begin shifting to easier and easier gears when on the flats.
IMHO shifting technique when going up hills is much more important. I've found it better to shift a little early than late. I've seen a lot of chains dropped from a poor shift of the front derailleur when climbing a hill. In fact that happened to me this past weekend. I was climbing out of the saddle up a small hill in the big ring when two dogs jumped out in the road in front of my. I slowed to avoid hitting one and when I tried to shift the FD down, I dropped the chain. Lucky for me those dogs are friendly.