IG, you don't have to cancel anything. But before you close your credit card account, just call up your insurance companies and tell them that going forward you would like to use a different card for payment and provide them with the account number. You can actually call them after you close your credit card account but I think it is better to do it before you close it because if a bill payment comes through after you close the account and gets rejected, the insurance companies might charge you a fee.