Shipping costs end up in the $500 range from what I've heard. I've also heard one person had some shipped for $200, but only from a single source.
Certain airlines do, and certain ones don't. A good person to ask about shipping would be Jenny Irwin (WNTMousery on here) she has shipped more than any one person I know of!
Shipping via American Airlines was $201 just for the ticket last week. That does not include the cost of the crate, mice, gas to and from the airport, parking at the airport, etc.
It is not a huge hassle using AA but sometimes the folks don't know their own rules. You do NOT need a health certificate with American Airlines when shipping mice, rats, hamsters and other rodents because they are NOT cats, dogs or primates. I had to point this out to a very confused clerk at the LAX airport last week who had to call his supervisor twice before we got it straightened out.