Just curious, wouldn't your credit card transaction slip have a spot for them to sign? Unless, I just realized you may be using a built in credit card reader, just the simple black swipe reader. In that case I understand your dilemma.
We are having the same issue here with stolen cards. 1 trick they are doing (to make you aware) is taking a stolen credit card, deactivating the magnetic strip and handing it to you to swipe. You swipe the card but nothing happens, it doesn't read it at all. They then tell you they have been having issues with it and ask if you can just manually punch the numbers in since it can't read it. Never do that, that's the trick. They will then report it as a stolen card and since you manually punched the card numbers in they can tell the card wasn't present for the transaction. You'll be out your merchandise and the money too. If they don't have an ID for a purchase over $40 we tell them sorry. Also, always try to get them to do DEBIT on larger purchases. A DEBIT transaction is much safer, only the true user will know their password.