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We consider the transmission and reflection of electromagnetic waves by an obstacle inside a waveguide. The method employed is an adaptation of the null‐field approach (T‐matrix method). The geometry is more or less arbitrary, but only for a waveguide with constant cross section can we obtain the scattered field in a not too formal way. For a circular cross section we derive comparatively explicit expressions for the transmission and reflection coefficients of the obstacle, and we give numerical results for spherical and spheroidal obstacles in rotationally symmetric geometries. As an important part of the theory, we have derived some apparently new transformations between the cylindrical and spherical vector waves and also expansions of the free‐space Green’s dyadic in cylindrical vector waves.