Sheryl:
"Neither frequent flyer miles nor awards have any cash value."
Actually, frequent flyer miles and awards have cash value (emphasis on value), just they do not have any tax basis allocated to them. Generally, for a charitable contribution, except for certain types of appreciated property such as securities, you are allowed to take a deduction for the amount of your basis (generally what you paid) for the item.
In the case of frequent flyer miles and/or flyer awards, since you generally have not paid anything for them (disregarding service fees/delivery fees etc.), you cannot deduct anything if you donate them

.
If you wanted to be REALLY AGGRESSIVE, you could say that when you purchased the airline tickets on which you originally earned the miles, you allocated some of the ticket's purchase price to the frequent flyer miles ( @~$.02/mile) (ie for a $500 ticket, you paid $400 for the flight, and $100 for the resulting frequent flyer miles), and then take a deuction for that amount. I wouldn't recommend it.
Cheers