I don't think I "test" potential partners or people I date, but I certainly pay particular attention to some things that are important to me, such as the way the person communicate with me (passive-agressive shit: you're out; inability to communicate needs/frustrations/desires in a grown-up, mature way: you're out; etc.),
the way they interact with other people (how they treat service people such as waitresses, baristas, etc. says a lot to me), the way they interact with my friends/their friends, the way they talk about people around them, etc.
So, it's not so much about "testing" them as trying to figure out what kind of person they are based on how they interact with me and others.