These are pretty rare, mostly falling under the Bulova Precisionist brand. I've grown very interested in them.
A typical quartz watch uses an oscillator that vibrates at a rate of 32,768 beats per second. That's 2 to the 15th power, and it's a very common number in digital electronics and computer science. It was selected in watches because it's just high enough that people can't hear the crystal vibrating.
Greater accuracy can be achieved in a couple of ways. Any crystal rated at a nominal 32,768 hertz will have a certain margin of error; manufacturers can buy crystals that are rated to be within 0.1% of their nominal rating, 0.05%, etc.
That affects accuracy. The closer the producer of the crystal warrants it to be to 32,768 hertz, the better the watch will be. Swiss quartz movements typically use 32,768 hertz crystals that are very close to their nominal ratings.
Another way to increase accuracy is to go beyond 32,768 hertz. The Precisionist line uses a 262,144 hertz (i.e. 2 to the 18th power) crystal. A 0.05% error, for example, will have less impact on accuracy at 262,144 hertz than at 32,768 hertz.
I have had my eyes on a Precisionist or something similar for a few years now. Up until now, I'd had a hard time finding one I liked. But there are some nice-looking examples out there now.
I like this one except for the goofy lock-down mechanism on the bezel:
Why not just offer a standard unidirectional bezel? Seems overly cute to me.
This Precisionist is pretty much beyond reproach, though:
The only real criticism I have is those four hex nuts.