Learn to play the harmony of any tune you are learning in double stops, and then be very judicious about where you use them. I do a lot of playing in duos and trios without a chordal instrument, and when you feel like you can play the double stops in tune, they can be a really nice texture to use for variety while supplying some extra harmonic information. The rub is that when they're out of tune, they usually make everything sound worse. Still doesn't hurt to practice them, though, as you never know when they'll pass the tipping point and be usable.
Also, listen to as many duo/chordless trio recordings as you can and check out what other players do. I found that this really helped, especially because before I did this I imagined they were doing all kinds of impossibly difficult things when in truth there was much less of that on the recordings than i imagined. Last, be patient. I've been on a kick for a while now doing duo sessions with Dave Klingman (a great local clarinet player), and when it's on, the results are some of the best music I've ever been a part of. Something about all of that space brings out creativity once you get past the fear of too much space.