I think that your escape options are really going to depend on what kind of side control your opponent has you in. You options from modified side mount (Twister Side Control as shown in the newest MTS) are much different than those available to you when your opponent is in traditional side control, whether the knees are tucked in against your body or not, and judo side control.
As a principle, as Bobby said, get a nice frame in on his hip and neck, or try to use heisman-style grips on their bicep when they try to cross face and on their tricep when they go over your head / turn to Twister Side.
If you want some links to good side control escape videos, or a much more detailed breakdown of escapes that work...hit me up.