[Arkcon]

Both ships are exploring space for a reason, yes? You need to mine asteroids for mineral resources, need new worlds for colonies, etc. So just appear to go about your business, and watch that other ship. You may be able to work out a collaboration, and peace may grow from that.

Heavy Metal magazine used to do this thing called "Galactic Geographer" or some such foo. It was sort of a sci-fi take off of National Geographic magazine. It discusses humanities first contact with an alien race, centuries before the fictional excerpt occurs:

A spacecraft exploring deep space asteroids for usable metals finds something on the sensors -- metallic, and moving. First slow, then fast, sometimes random, sometimes not. It's a spaceship. The two ships tail each other for a while, playing "Crazy Ivan", hiding from each other, then catching each other. Finally, they faceoff. There are no universal translators. They "agree" to meet in an EVA, they bring scientific instruments to study each other. They could have bought weapons, but didn't. After study, they were no closer to understanding each other than they were before.

Now the Galactic community spans hundreds of star systems, and has dozens of species -- but these first contact aliens were never seen again.