Amex used to have a plan where, for $15 per rental period, they would cover liability if you paid for the rental with your Amex card. The $15 fee was added as soon as the rental was charged to the card. They had a similar plan for trip cancellation and/or delay, and lost baggage. This was on the Blue Cash card, which had no annual fee. It's been several years since we've used that card, so I don't know if it's still available.