I spotted this rainbow yesterday (too late) and this was my best shot (through a window). I processed to bring out the rainbow without being too heavy-handed. It looks over-processed to me, but you can definitely see the rainbow. Processing is just with DPP: cropped a little; moved the left/right thresholds rather than playing with exposure; and maxed out the RAW and RGB saturation. I also applied the standard Digital Optimizer, but I don't think it really made much difference in this case.
I'm wondering if there's something else I could do?
As an aside, this is the second rainbow we've seen in the past week. The first one was a full rainbow and more vibrant, but I was driving at the time (and didn't have my camera).
50D with 70-200 f/2.8L II IS @ 70mm 1/250" f/11 ISO400
Original (after crop)
Processed