1. A method implemented by a computer, the method being for tuning a lithographic apparatus using a corresponding differential model that predicts changes in imaging behavior due to changes between two or more lithographic apparatuses, the method comprising: maintaining a lithographic process model characterizing imaging behavior of a lithographic process for a given layer of a wafer using one of the lithographic apparatuses, given particular values for the set of tunable parameters on the one lithographic apparatus; generating a simulated wafer contour in the given layer using a design layout and the lithographic process model based on a set of values of the set of tunable parameters; identifying discrepancies in the simulated wafer contour against a reference corresponding to the set of values of the set of tunable parameters and a different one of the lithographic apparatuses; quantifying the discrepancies with a cost function; and performing iterations of the generating and identifying steps to minimize the cost function and obtain calibrated parameters of the differential model, wherein each iteration uses a different reference corresponding to a different one of the lithographic apparatuses, wherein one or more of the maintaining, generating, identifying, quantifying and performing steps are implemented by the computer.