|"You f'd up a long time ago." -Kurt Osiander, eloquent as always.|
Countering the Side Control Kimura
First, as your opponent tries for the kimura, attempt to grab your own collar; not your belt, not your leg. (aka, if grappling with a Gi, use it!)
If you've managed to grab the collar, grab the far leg behind the knee, scoot out to a north-south, and spin out of the kimura and regain guard.
(Failing the above)
...but you done f'd up and are now stuck in a side control Kimura
You are trying to keep him from stepping over to lift you and cranking the kimura home.
Bridge up and straighten your arm at the same time- this will open you up momentarily for another armlock, so tuck in, frame out, and regain your guard. This one is much less likely to work than the first defense.