We propose a convex optimization procedure for identification of nonlinear systems that exhibit stable limit cycles. It extends the “robust identification error” framework in which a convex upper bound on simulation error is optimized to fit rational polynomial models with a strong stability guarantee. In this work, we relax the stability constraint using the concepts of transverse dynamics and orbital stability, thus allowing systems with autonomous oscillations to be identified. The resulting optimization problem is convex. The method is illustrated by identifying a high-fidelity model from experimental recordings of a live rat hippocampal neuron in culture.