Being given advance notice of more than a day or so, usually, you should just thank her for the courtesy of telling you about it, and you should ask her if she could recommend any friends who might be available, or suggest an alternative time to meet her.

If she has to cancel with very little to no advance notice, or worse, stands you up and apologizes later, then, IMHO, she owes you a little consideration.  If she's good, and she cares about customer service, she should offer you either a small (say $50 -$100) discount, or a slightly longer session (such as an extra 1/2 hour).  The mere offer would indicate someone with an above average approach to customer satisfaction, and would suggest that you certainly try again to book time with her.

But she should offer it to you.  If you suggest it directly, you sound cheap.  But you can diplomatically steer her that way.  Simply say that you were dissappointed you couldn't meet her, and would still like to, and would she be amenable to treating you nicely in consideration of your inconvenience in a future session.  If she does not offer something, it tells you that you should move on.

I usually try to have a back up plan in place.  Like, a massage parlor or something.

But, if this gal is a well reviewed provider, I would hope she would either give a discount to you or extend your time with her.

One observation....a family emergancy could be something major or just mother nature paying an unscheduled visit.

I've had 2 providers cancel on me at the last minute without even a phone call or e-mail, after confirming our appointments 2-3 days, not hours, in advance.  Both were reputable providers with good reviews in both TER and TBD.  Needless to say, I was pissed at such a lack of customer service.  Providers request to book appointments in advance, which means that thay ask us to respect their time.  Well, that rule goes both ways also.  Don't ask us to book appointments days in advance, and then not show up.  One provider "got sick" that morning (hmmm, sick in the morning, evening appointment, I think there was plenty of time to notify me) and the other provider stayed overnight at a girl friend's house and "forgot."  I will not see either provider ever, since they did not respect my time.  Ask for a discount since it was their end for cancelling; but me, I would stick with the reliable ones like Julia.  If I could, I would post both of the flakes on all boards.  EOM.