I don't provide back up care, exactly. I have it clearly stated in my handbook/contract, in bold even! It is THE PARENTS responsibility to have alternate care available. If I am closing for a personal or vacation day, I give lots of notice. Usually a month or so. If I have to close in an emergency, I call them as soon as I know that it will be happening. I have called before 6am, so that they have time to figure it out.
Truthfully, if i met with a family that said "You're it, you are our ONLY available caregiver..." I probably would not take them on. Unless they are totally okay if we have to close on short notice. I just find that some people say "Oh, no problem" but when it comes down to it, they get really cranky. That said, I really try not to close, as I can totally understand that it leaves the parents in a bit of a pinch.
I do have my husband available if need be, for trips to the bank, doctors appts, etc. When I was pregnant, and had umpteen appts, he was always there. I also tried to schedule them during nap time. Parents were all made aware, and no one had any issues. My hubby is home quite a lot during daycare hours, and so all the kids and the parents are familiar with him.