UA does not charge a fuel surcharge on an award ticket. All SQ awards must be booked by calling -- SQ inventory will not show up on the web -- so if you get an agent who insists upon charging the surcharge, HUCA.

IIRC, there have been problems in the past where agents tried to collect surcharges that were coded under YR instead of the more common YQ. I'm not sure if that's happened recently.