You can sometimes get lucky by using united.com. Be sure you are in expert mode and you can sometimes see availability (check out Oz's link on the fare codes.) Go to the Award travel. Note you sometimes have to book a first or economy to see the business buckets. However, if there are no award seats, you can't see availabilty.
Don't forget in expert mode you can check out UA availability like you did before. You can even access the seat map - just make a dummy booking. You only need to pick the flights and select a traveller profile. It will be at the bottom to select seats.
[This message has been edited by LHR Tim (edited 11-09-2003).]