Second-order cone programming is a highly tractable convex optimization class. In this paper, we fit general second-order cone constraints to data. This is of use when one must solve large-scale, nonlinear optimization problems, but modeling is either impractical or does not lead to second-order cone or otherwise tractable constraints. Our motivating application is biochemical process optimization, in which we seek to fit second-order cone constraints to microbial growth data. The fitting problem is nonconvex. We solve it using the concave-convex procedure, which takes the form of a sequence of second-order cone programs. We validate our approach on simulated and experimental microbial growth data, and compare its performance with conventional nonlinear least-squares fitting.