Simulation models that are expressed as ordinary differential equations contain a large number of constant parameters. It is often important to determine if there are physically permissible combinations of parameter values that can produce periodic solutions. Only occasionally is it possible to establish an analytic criterion for oscillations, and trial and error searches through a large dimension parameter space are often computationally prohibitive. This paper presents an approximate computational procedure that uses constrained optimization techniques to greatly accelerate the search for oscillatory parameter values.