Not sure about the United card, but the Sapphire card has Trip Cancellation insurance which will refund you the amount of the ticket due to disease or physical illness of you or an immediate family member. This benefit covers up to $5000 (but you must relinquish any unused travel credits/coupons).

It also has Trip Delay insurance which will pay for a hotel (and food, etc) for a delay more than 12 hours. This benefit is for up to $300.