To see that space on .bomb (UA.com), first enable the "expert mode" in your UA profile. Click on "My Profile", and then click "My Travel Information". About half-way down the page you will see an option for novice or expert. Set it to expert.

Then follow these steps:

1) Click the tab for an award search, enter your cities, dates, etc, and click go
2) When the flights load up, click on flight details for the preferred flights
3) For domestic flights on two-cabin aircraft (F&Y), you'll want to look for NF. If it's a three-cabin aircraft, i.e. an international flight, or domestic sector using international equipment, make sure to look for NC. If you see NC>0, that means that there is space available to upgrade from Economy to Business. If you had a paid Business class ticket, you would look for NF>0 to upgrade into First.