The robustness of a template set for cellular neural networks (CNNs) is crucial for applications of VLSI CNN chips. Whereas the problem of designing any, possibly very sensitive, templates for a given task is fairly easy to solve, it is computationally expensive to find optimal solutions. For the class of bipolar CNNs, we propose an analytical approach to derive the optimally robust template set from any correctly operating template. Furthermore, our method yields a theoretical upper bound for the robustness of the CNN task.