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An inverse problem of continuous wave electromagnetic scattering is considered. It is assumed that the incident and the scattered fields are given everywhere and that the material surface properties satisfy the Leontovich boundary condition. Applying the concept of electromagnetic inverse boundary conditions it is shown how the shape and the averaged local surface impedance for spherical monobody and two-body scattering geometries can exactly be recovered. To enable accurate inversion for the multibody or general spherical case, analytical continuation methods in three dimensions are introduced.