We have found that most of our au pairs who have come from central and eastern Europe mainly provide written/paper based references that are from people who don't have an email address.
If you insist on an email address then you may rule out a perfectly valid reference from a girl's neighbour who has never worked with a computer in her life, and force your prospective au pair to ask her friend who just graduated with her (and has a job that comes with a work email address) to write one for her instead.
Email from work based email addresses probably works better with other English speaking countries that are part of the Youth Mobility scheme, where it is wasier to call and check an English speaking person.
Reference checking by email is flawed anyway as every reply can be delayed until the subject of the reference has been contacted to concur what should be said. I'm not saying everyone would do this but you can imagine can't you...
Supposed Referee: "Hey Maria it's Ana. Guess what - I got an email from some English family asking about you. What do you want me to say?"
Maria: "Oh great - ok - can you just tell them that I was babysitting for your two kids ever since you went back to work in 2006 - tell them I used to take them out to the playground, buy them ice creams and used to sing songs and read books to them - that woild be perfect"
Emailing a reference doesn't give any opportunity to ask any on the spot questions.
Unless you focus on English speaking au pairs from the Youth Mobility scheme then all others will come from non-English speakign countries. It means references obviously will be provided in a foreign language and checking them will be a job for someone who speaks that language.
As TennisFan says - it's a long hard process. If you have all the time in the world and don't mind the frustration of people letting you down then you'll be fine. If you want a thorough job done by people who do it every day for a living then use an agency. After she arrives you've also got their support and the security of knowing if things don't work out you can find a replacement easily.