What is the fine for noncustodial parents claiming the exemptions?

First, non custodial parents are not eliminated from claiming the exemption for children. However, only the one that meets the qualifications of the tests for claiming a dependent as either a qualifying child OR a quailfying relative may take them, legally. Fairly easy problem for the computers to spot especially if 2 returns claim the same person as an exemption. Common sense should tell you that something as easy as saying 2 instead of 1, on an issue many are so cognizant of and not novel in any way, has a fair number of safeguards built in. First, both returns have the deduction denied (it may obviously occur after refund has been received), and explanations need to be found. Someone will end up with a penalty and interest, although as the benefit received is farily samll (generally about $750 really), these aren't going to amount to too much if paid promptly. One if not both will end up with their returns reviewed, and likely be up for further forward and backward scrutiny of all their tax positions for some while. Obviously there are actual criminal penalties possible, but unless more turns up or the problem is repetitive, that is unllikely for a "mistake".