On 2008-06-15, John Smith wrote:

I measured the voltage across the black and either of the two traveler
screws and it was 0.

This is to be expected, as there should be no voltage drop across a
switch, since there is no load.

However, if I measure the resistance, it does seem to work (0
between the black and one of the traveler screws and infinite if the
switch is flipped. Same for both traveler screws.)

This suggests the switch is fine and you have miswired the circuit.

Cheers, Wayne