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You can use any great circle distance calculator that allows you to enter latitude and longitude. Here's one:
http://williams.best.vwh.net/gccalc.htm
(for "Earth model", select spherical). Since this is a javascript calculator, you can view the source and modify it to suit your needs if you feel like messing around in code. Just enter SHA (or GHA) for longitude and Dec for latitude.

Great circle distance doesn't depend on the coordinate system, so you could also enter azimuths and altitudes instead of SHAs and declinations. This is handy if you want the refracted distance. If you use a standard planetarium software app like Stellarium, you can set it for some location and time and read out the altitudes either true or refracted and then enter them into any great circle distance calculator.

I've said this recently so I apologize for repeating, but you can get the refracted distance for any pair of stars when both altitudes are above 45 degrees to a good approximation by decreasing the true great cirlce distance by 1/3000 (a tenth of a minute of arc for every 5 degrees of distance).

-FER

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