Originally Posted by AdamK

I don't know about other airlines, but here is United's policy.

UA WILL REFUSE TO TRANSPORT...ANY PASSENGER...WHO REFUSES TO PERMIT SEARCH OF HIS/HER PERSON OR PROPERTY FOR EXPLOSIVES OR A CONCEALED, DEADLY, OR DANGEROUS WEAPON OR ARTICLE....SUCH CARRIER WILL, AT THE REQUEST OF THE PASSENGER, REFUND IN ACCORDANCE WITH RULE 260 (INVOLUNTARY REFUNDS).

Rule 260 provides for a full refund of the initial ticket price (or a commensurate fraction thereof depending if the ticket has been partially used).