For the solution of the scattering problem for time-harmonic electromagnetic waves with boundary conditions for the normal components of both the electric and the magnetic field, an integral equation method proposed by Gülzow in 1988 is reconsidered. It is made more concise, made symmetric with respect to the electric and magnetic field, and also extended from the classical Hölder spaces to a contemporary Sobolev space setting. For this regime, new reciprocity principles for scattering of plane waves and dipole fields are established and a related far field operator is discussed. Finally, the corresponding inverse scattering problem to recover the shape of the scatterer from far field data is discussed with the main emphasis on uniqueness results.