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This paper presents a generalized continuum design sensitivity formula that is applicable to any shape design problems of high-frequency devices in frequency domain. The derived sensitivity formula is expressed in terms of surface integrals over a part of the interface between different materials and of the conducting boundary undergoing shape modification during iterative design process. Using the proposed approach, it is easy to deal with the shape optimization concerning conducting surfaces as well as dielectric contours. The method has been successfully applied to the optimization of high-frequency waveguides where the numerical implementation is thoroughly investigated from the viewpoint of constructing adjoint systems and calculating sensitivity values.