One of the best ways to get people interested in your comic is to have your character guest star in someone else's comic. This is not as easy as it may sound.
The first step is to talk someone into guesting your character. This can be simple or complicated, depending on how well you the person. The ideal would be a reciprocal deal, where characters from both strips show up in the other, but that is something that can be negotiated. You may have to promise something, such as money or some special favor, but some people will do it for something as simple as a link. However you do it, do it; it's some great publicity for both sides and it can build some interesting links between the two comics.
You have to work out some sort of justification. The simplest is the “face in the crowd”, where the character just appears in a crowd of characters. The most complicated is the “multiversal cafe”, where characters from a variety of universes show up and either just meet or get assigned to some Grand Quest. This is not advised unless you have a story that works for everyone, and that everything has been worked out. Slightly better is the “quick trip”, where one character shows up in the other strip, does something quick, and then either goes back to original universe or recedes into shadows.
The one major detail worth debating is what similar characters will do when they encounter each other. There are a number of ways of joking around with it, ranging from the characters purposely ignoring the similarities even as other characters comment on it, to one character taking advantage of it, taking over the other's life and, um, sleeping arrangements. There can also be some confusion between the two, as well as one claiming to be the original. Conflicting characters can be handled as needed, but characters with similar designs need to be handled, and it provides for some comparison between the two strips, so have fun with it.
Do not forget to cross-advertise a little. The idea is to get some marketing out of this, and it will not help if it just happens in the background. Post a note on Facebook, tweet it, and let people know! This could be something fun, and it helps if you advertise a little. This can be a great way of getting two or more strips together, and having some fun with all characters and concepts involved. So get going on corssovers, especially if they make sense in the normal world.