If you are fighting someone much bigger, or someone with great kimuras, or if don't feel comfortable with that move, I saw a video by Rener and Ryron on how Ralek beat Sakuraba, and how he focused on kimura defense. Basically, he would just drop that shoulder to the mat and put his weight on it, so that Saku could not free the hand. Then he would slowly work the pass.
I like to go a little heavy on the kimura arm (be careful not to over-commit or you can be swept) and use the other hand to pry the knee, rather than the hip. Think of the basic pass from 1/2-G when you turn towards the legs (like TSC except from 1/2-G). Just walk the trapped foot up to his butt so that his 1/2-G is sitting on your knee like a ledge, push the knee off to free your trapped knee, and then either scorpion tail your trapped leg backward (towards the kimura arm side), or I really like to drive it across into quarter guard and go heavy. Then, you can either use a traditional pass or twister roll.
Does that make sense? I hate trying to write out moves - I always miss something or get really deep in the details so that it is hard to picture. I need to get a video camera.