If she has an emergency trip to attend to,  that probably means that she's also too busy with other pressing matters to respond to e-mails right away.  I wouldn't think much of it.  Give her a couple of days to take care of what ever she needs to, and then if you haven't heard back from her send her another e-mail or phone call.  If you then get no response I would start the search for somebody else.

Read Traveler 10's post down below!

Well, I'm just joken withya, but you never know. Good chance it has nothing to do with you.

Call me a cynical type, but I am often skeptical of these last minute "emergencies". At least to the provider's credit, she gave you a one day heads up, so that you still had some time to arrange for another date on the following day which would have been your original date day.

The cause: point being that whatever the reason for the cancellation, it will simply drive you bonkers trying to think about the cause of it! Learn not to focus on merely one provider and keep in the back of your mind that this kind of stuff happens (getting stood up) and as long as you conducted yourself with great manners and integrity, just thank her via email for spending the time communicating with you and wish her well with her "emergency" and future endeavors. If she gets back to you after a few days, then decide for yourself as to whether you wish to re-schedule. If not, do not cheapen yourself by chasing her.

The causality: IMO, she did you and another provider huge favor! Remember that when one provider decides not to see you for whatever reason as long as the reason is not display of creepiness or bad behavior emanating from you, then another door opens to you as you are no longer transfixed solely on one provider (do you think that they go around all day thinking about one client that they have not even met?)  IMO, the correct attitude and discipline in here is to concentrate on the causality of this event, i.e, find a willing provider, do your homework and spend your $$$ with someone who is both willing and able to see you. If you wish to give her a second chance, then fine, as I do believe in second chances and redemption, but you'd be a fool to chase her.

BTW, my advice also applies to the providers who get stumped by certain clients. Casino's advice is always a 2-way street