Just to confirm what Tim and others have said and add an alternative, unfortunately, according to the baggage insurance department, one is *not* covered for award travel, even if the taxes are paid in your card. You must put the full fare on the AMEX card, and if there is no cost for the fare itself, they will not cover it.

One can purchase the insurance separately. It starts at $20.00 per person for the lowest coverage and goes to $50.00 per person for the highest coverage (not sure either option is worth it). For more info, call 800-332-4899 for that specific department.