We show experimental and theoretical results for enhancement of nonlinear transmission (NT) in moderate finesse cavities filled with nonlinear organic materials (NLOM). Our design for enhancement of nonlinear transmission using micro NLOM cavities compared with reference samples of the same material show that single cavities can enhance the nonlinear response by a factor of 10 or greater under high-absorption conditions. Further enhancement can be achieved in multiple-cavity structures. Other advantages of the cavity structures for nonlinear transmission, such as a higher damage threshold and a broader NT band, are also discussed. Our initial experimental results show a threefold reduction in the nonlinear threshold fluence in a single cavity device compared directly to an identical sample without mirrors, in qualitative agreement with our calculations.