From Burning Wiki
There have been a number of useful discussions about failed Circles tests on the forums, and how to spin the Enmity Clause into into interesting situations.
Thor on the breadth of the Enmity Clause
Just to be clear, when a GM invokes the Enmity Clause, that enmity doesn't have to be with the person (or sort of person) that the player was attempting to reach with Circles. The GM has broad latitude.
If you're circling up your gang boss to gain support for some initiative, you might find him and he may like the idea. But then his boss comes down like a ton of bricks. He shuts the plan down and now he's got his eye on you (and your boss) in an unfriendly way.
Or you go to Circle up your gang boss and surprise an assassin just as he's making a move on the boss. Maybe it leads to a fight right then and there, and maybe the assassin melts away, only now he's going to gun for you too because you've seen his face. If he's still alive, your boss will be grateful, but you've now got bigger problems.
Or maybe you go to see the boss and someone who's staking out the joint (whether from the constabulary or a rival organization) now know that you're a lieutenant and will start keeping tabs on you as well. It may be several sessions of play before there's a confrontation.
A quick addendum from Luke: "Neither does the text say it must be the same person you were searching for."