Not sure how the interest would be credited after a death. The income tax paid on interest of an estate is very high.
CDs with terms over 1 year are issued 1099-OIDs (Original Issue Discount). There's no actual interest payments nor is there technically interest (1099-INT) for tax purposes but rather a discount on the face/maturity value which becomes income upon maturity (like a zero coupon bond). Although since 1984 the tax code requires individuals to amortize the taxes on this income over the term of the bond/certificate (otherwise it'd be effectively tax deferred like an IRA), I'm not sure what the requirement would be for an estate.
However, for an estate I now also understand that since the account would be POD and the "record holder" deceased, the estate would not even be liable for the tax because the estate would not be the legal owner of the account/income (because the POD provision takes precidence over probate). But, until the bank is notified of the death, the estate would still be receiving "1099-OIDs showing amounts belonging to another person" and thus would still need to file a tax return as a nominee and issue a 1099 to the beneficiary (who'd be the actual legal owner of the unclaimed income).
In general, any time someone receives a 1099 for amounts that do not belong to them (or are held on another's behalf) they need to file a tax return as a nominee and issue a 1099 to the actual owner. So in my example the procedure's the same regardless of if it's my relative (who opened the account on my behalf as a middleman) or his estate (which would simply be receiving erroneous 1099s due to the bank not yet having the necessary paperwork to retitle the account) who's receiving the 1099: file as a nominee and issue a 1099 to the actual owner (me).