Flying through CB's is obviously never a good situation.
The best thing to do (certainly from what I have been told on the 737) is to increase the WX radar range and navigate round them, of course advising ATC at the time. You have to increase the range on the radar, there is nothing like dodging one small one, but not seeing a massive one just off screen straight in your path. This of course applies to enroute CB's, now CB's on final approach.........
The 737NG has something called PWS (predictive windshear), it notifys the pilots (below 2,300ft I believe) of any windshear ahead of the aircraft. I have not seen this in operation, apart from a demonstration during my type rating.