Depends on what you got for backing, if it's just a guitar, I'd steer mostly towards implying the chords you're playing your melody over. Either by outlining the arpeggio, playing the root note with one finger, and melody with the other, or open strings.

I play mostly acoustic, and I play solo by changing into a dropped tuning, like DADF#AD, and it allows me to play a melody and a harmony simultaneously. If you're playing electric, you could try to have a little harmonic idea, with fills in between. For example, The Guitar from the verse of Crazy Train, by Ozzy Osbourne. The Guitarist plays a few chords, then inserts a fill, and it stands well on it's own.

Hope thats helpful! Good luck with your endeavor!