Katy, I don't know if this is relevant as I only recruit aupairs. But I too have to sift through lots of applicants without even the benefit of an interview, beyond a phone call. So far, I have generally been satisfied with my aupairs, despite a hit-and-miss recruitment process.
I rely a lot on references, preferably in a very similar previous role. Call them up (be alert to false references by cross-checking personal details over phone) - references are a very good barometer for personal qualities and to get a feel for a candidate. Sometimes, it is as much what is unsaid as what is said. But be as direct and specific as you want to find out what you need.
Little things, like whether their CV is rife with typos or neat and well-presented. How punctual they are for the interview, how quickly they respond to your emails/calls and how they address your queries. If you ask for references, how quickly can they get the details for you.
Shows keenness, organisation and thoughtfulness.
That allows you to sift through for a shortlist to interview.
Then at the interview, I don't have many tips because I don't really have the luxury of face-to-face interviews for aupairs, go with your instincts, amongst other things.
I like the trial session. One tip for interviewing nannies is to leave the candidate alone with the children (I hope that is allowed, with other carers present) and go out for a short while on an excuse eg answer a phone. When you come back, see whether the candidate has taken that chance to interact with the children. Someone who is keen on children should. Which is more than half the battle won.
Good luck!