One may remove the whole distributor housing fairly easily
so as to be able to remove the old, broken screw. On older
Hondas, it's typically just three large bolts that hold the
housing on. The whole housing rotates to set the timing, so
remember to mark the housing beforehand. That's a bit tricky
the first time, but once you free the housing, it will be
obvious.

Remove distributor to expose the broken bolt.

With a sharp punch or (small sharp chisel) and a hammer, gently drive the
remnant counterclockwise. It should come out easily. The punch should be
placed as close as possible to the edge of the remains of the bolt.

Does any length of the bolt stick out from the back side of the hole?  If
so, then you might be able to turn it with some needle nose vise grips.
Another option would to remove the distributor and drill it out with a left
handed drill bit.  Be sure to use a small punch to make a center mark on the
remains of the bolt so that your drill bit will be centered.  Using a left
handed drill bit will loosen, if not completely remove, the broken off
screw.  However, a regular right handed drill bit will simply tighten the
screw and make it more difficult to remove.  If you decide to drill it out,
then you should protect the rest of the distributor with a rag or by some
other means to prevent metal flakes from interfering with the magnetic
pick-ups in the distributor.  If there's enough screw for a small punch to
grab as Tegger suggested, then that might be the best way since it will
reduce the possibilities of metal flakes getting lost inside the
distributor.  Note, that it would probably be best to use a timing light to
reset the timing after after you put the distributor back.

Eric