  We discuss the Casimir effect for boundary conditions involving perfect
electromagnetic conductors (PEMCs). Based on the corresponding reciprocal
Green's tensor we construct the Green's tensor for two perfectly reflecting
plates with magnetoelectric coupling (non-reciprocal media) within the
framework of macroscopic quantum electrodynamics. We calculate the Casimir
force between two PEMC plates in terms of the PEMC parameter M and the duality
transformation angle ${\theta}$ resulting in a universal analytic expression
that connects the attractive Casimir force with the repulsive Boyer force. We
relate the results to the duality symmetry of electromagnetism.
