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Plausible inference is a growing body of literature that treats stochastic simulation as a gray box when structural properties of the simulation output performance measures as a function of design, decision or contextual variables are known. Plausible inference exploits these properties to allow the outputs from values of decision variables that have been simulated to provide inference about output performance measures at values of decision variables that have not been simulated; statements about the possible optimality or feasibility are examples. Lipschitz continuity is a structural property of many simulation problems. Unfortunately, the all-important—and essential for plausible inference—Lipschitz constant is rarely known. In this paper we show how to obtain plausible inference with an estimated Lipschitz constant that is also derived by plausible inference reasoning, as well as how to create the experiment design to simulate.