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The paper presents shape-preserving response prediction, a new technique for efficient design optimization of microwave circuits. It allows us to estimate the response of the microwave structure being optimized (fine model) using a computationally cheap representation of the structure (coarse model). The method has excellent generalization capabilities and does not require any extractable parameters. Here, the technique is developed in its simplest form that can be applied in case of certain class of microwave structures, particularly bandstop filters. The robustness of the proposed approach is demonstrated using two microwave design optimization problems.