I typically try several internet streams of stations that I suspect it may be due to hints dropped in the broadcast, like references to places, stores, etc.
I also record the audio so that I can go back and hear that elusive ID should it "zip by" and I don't catch it.
Most of the time I get the ID during my listening, but on some occasions I have to get "creative" with an internet search.
ID'ing this way may not be everyone's cup of tea however, and I can respect that, but it is a method I have used for my personal logs.
Your tastes may vary...