Thanks for the very quick replies. I've discovered that it's not subtracting the dates that's the issue, but the fact that I'm embedding this inside another formula. The complete formula I'm trying to use is:
Where A9 is a date, and B9 and C9 are two times. I only want the difference between the two times to display if the the date in A9 is today or a date in the past. This works, except if the difference between the two times is 0 minutes, the formula returns -00:00. If I just do B9-C9, Excel correctly displays 00:00.