Couple more options for tension:
They want something REALLY REALLY REALLY bad, but for some reason they can't ask for it -- or can't have it even if they did ask.
They don't notice something that the audience HAS noticed (like in a horror movie when the monster is sneaking up behind the protagonist, or if someone drinks a glass of unboiled water during a cholera outbreak because they don't know about germ theory)
Takes a risk (or otherwise does something they "shouldn't" do) which the audience has to sit through for a prolongued period of time (e.g. slips away from the party to go into the host's private office and rifle through their papers before the guards catch them)
Loses when they thought they were going to win