An obituary is a good idea; so try that. But you may need a death certificate anyway.
Who is the executor or attorney involved? That person will have access to death certificates that have already been requested for other purposes. You may be able to send these people a photocopy of one of the existing certificates, instead of going to the courthouse to get a certified copy (which may cost some money).
Also if there is a lawyer involved in taking the estate through probate court, try giving the company that lawyer's name and phone number. It doesn't matter that there's no money to settle the accounts, that's who's settling it, not you!