How much available credit should I leave on my father’s credit cards?

For freezing one's credit here is a good reference guide: https://clark.com/credit/credit-freeze-and-thaw-guide

I would cancel one of the cards, especially if they have an annual fee. Hopefully one of the cards earns points (my CapOne card gives lots of points which automatically get applied when I make purchases on Amazon). Make sure no one else is joint on his cc account. You can put a freeze on his credit to protect him from fraud. You can cancel both cards if they have annual fees, and get a credit card through his own bank (assuming he has a checking account there). That's what I did with my 105-yr old Aunt. No fee and just a basic low limit. No debit card. Then, connect the cc to get automatically paid from the checking account. He doesn't need a high credit limit, he doesn't need to worry about his credit score. He shouldn't be needing any sort of credit at his age. Also, he should have only the minimum of cash in his checking account. The rest should be in a savings or money market or other easily accessible account. This also protects against theft or his own misuse of his funds. If you are his FPoA you will need to make sure his investment companies recognize your authority. I just had to do this with both my 95-yr old Mom and my Aunt. Not all the companies have the same PoA recognition protocols. One was a total pain in the rump and a lot of work. Do it now so that you don't have to do it in a crisis because there was *a lot* of back-and-forth, submitting and afidavit, notarizing (at a bank only), emailing, faxing etc. for that one investment company.

Zero limit = less risk. I'd use alternative ways to pay if possible.

There is no need for cards with credit limits where I live, as many alternatives exist. For bills: funds transfer via internet banking or direct debit. For online shopping: debit cards or pay in installments.

What do you typically use the cards for? If you only use it for his monthly expenses then at his age you probably don't need a limit much beyond that, any major purchases can be made using a cheque.