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We introduce a tuning space-mapping technology for microwave design optimization. The general tuning space-mapping algorithm is formulated, which is based on a so-called tuning model, as well as on a calibration process that translates the adjustment of the tuning model parameters into relevant updates of the design variables. The tuning model is developed in a fast circuit-theory based simulator and typically includes the fine model data at the current design in the form of the properly formatted scattering parameter values. It also contains a set of tuning parameters, which are used to optimize the model so that it satisfies the design specification. The calibration process may involve analytical formulas that establish the dependence of the design variables on the tuning parameters. If the formulas are not known, the calibration process can be performed using an auxiliary space-mapping surrogate model. Although the tuning space mapping can be considered to be a specialized case of the standard space-mapping approach, it can offer even better performance because it enables engineers to exploit their experience within the context of efficient space mapping. Our approach is demonstrated using several microwave design optimization problems.