Besides radio, SETI is also searching for signs of artificial technology in data from infrared (space) telescopes. The idea is that civilizations make good use of energy, and solar energy is the most abundant and easy to access. Fusion power for free. Fissile elements are mostly inaccessibly hidden deep inside planets. If a civilization absorbs a substantial part of a star's light for its industry, the natural star light would be replaced by redshifted waste heat radiation from that industry. Something we should be able to detect with today's technology.
Jason T Wright seems to be the one man driving force behind this kind of actual search today, within the SETI and wider science community. Here are some links to a talk, slides, a paper and a blog by Jason. Lots of galaxies have been studied, so at least it isn't common that civilizations extract most of the energy from entire galaxies. The universe might be too young for that.
Personally, I fear that our focus on life and intelligence as we know it, expressed in the in my opinion naive Kardashev scale may miss that there might exist completely different kinds of phenomena out there. Life on Earth is all just one single instance. We have no diversity, no statistics, but we do know that the combinatorics of chemistry is mindboggling. But we can only do what we can do, and it would be a bit strange if there's nothing like us out there, considering how extremely ancient and successful DNA-life is on Earth, which doesn't seem to have unique circumstances. A problem might be that biology seems to use all tricks, except radio.