What about stray radiation from beam power systems. Aliens might have free-electron GRAZERs orbiting their star, beaming power to the outer planets. They wouldn't be modulated necessarily. Of course their targeting would be very good, and there might not be any stray radiation.

Exhaust streams from propulsion systems, like pulsed-nuclear or antimatter rockets might be visible from a distance, possibly in the x-ray spectrum. Maybe they have a constellation of mirrors orbiting 200 AU from their star, bouncing a gamma ray beam, originating from a platform orbiting their star, back inward to a starship moving in a circle at 50 AU. A mirror on the starship would reflect the beam into space and gain momentum, moving faster and faster as it circles the star. Eventually, it might approach the speed of light, and then hurl itself into interstellar space. This process would give off alot of stray radiation in the gamma ray spectrum.

We might look for particle showers bleeding energy from high speed starships as they plow through the interstellar medium.

And how about just building a monster telescope that can SEE them, on their own planet, whether they are sending signals or not?