Oh, boy. I'm going through this drill right now for my mother's estate.
First, the executor of the estate should send each creditor that can be identified a letter identifying the account, date of death, and include a photocopy of the death certificate and the credit card cut in half. Send the letters by certified mail with return receipt, to the address for communications for each card. Keep copies of the letters. (A few cards will insist on a certified copy of a death certificate, but those are expensive. If they need it they'll ask for it.)
Actually, if there's an executor (or a personal representative in some states), they should send the creditor (1) the court order appointing them executor or PR and (2) instructions for filing a claim with the estate. Note that different states handle things differently, and the process may differ slightly from state to state.