Initially disappointed with the GH2's colors I work with both jpg and raw.
A few days ago I saw a post on dpreview's micro43 forum with settings by Robiro, and put them in my camera. I am very happy with them. This image represents a custom white balance made using the white target on X-Rite's color chart, using Robiro's settings. It was made from a raw image, converted in Adobe Camera Raw in the CS6 beta, just resized down. Here are Robiro's suggested settings:
"Keep the camera at +2/3 EV compensatio*, film mode: Vibrant, Intelligent resolution: High, I. Dynamic: High

With JPEGs, the camera will underexpose nearly all shots, even at +2/3 EV. This needs to be corrected in post-processing (Curves adjust). Also, all shots must be white balanced. That is a must (to get rid of nasty yellowish-greenish cast).

Keep the histogram always on. Whenever you see that only 60-70% of the dynamic range is used, keep increasing +EV compensation until you hit about 90% dynamic range usage.

Problem is that what you see in a viewfinder is NOT how JPEGs actually look like. The camera optimises what you see in the viewfinder. A horrible habit. "

*I do not keep the camera at +2/3 exposure compensation. I rely on the histogram to decide upon exposures and just lately have started using a set of bracketed exposures to decide upon the best interpretation of what I see. The automatic bracketing in the GH2 is very nicely implemented.

I know our eyes can play tricks on us, but when I look at the various shades of denim in this image, they look very much like what I see in my closet.