We consider well-posedness of TE and TM polarizations of time-harmonic electromagnetic scattering by perfectly conducting periodic surfaces and periodically arrayed obstacles. Inspired by recent studies on scattering by periodic dielectric layers, we propose a new radiation condition to characterize evanescent waves propagating along the scattering surface. Uniqueness and existence of time-harmonic scattering by incoming point source waves and plane waves from locally perturbed periodic structures are established under either the Dirichlet or Neumann boundary condition.