The recently introduced operator expansion formalism has brought new analytical power and computational efficiency to the scalar theory of rough-surface scattering. Extending this method to electromagnetic scattering from a perfectly conducting surface is the subject of this paper. This simplest of boundaries imposes a Dirichlet-like condition on the electric field component locally tangent to the surface; Maxwell's equations determine the normal component through a Neumann-like condition, which requires an inverse operator to the normal differentiator. The resulting formalism, while considerably more elaborate than the scalar version, is nevertheless orders of magnitude more efficient than existing matrix methods, so that problems of three-dimensional scattering from surfaces of multiscale roughness can now be computed accurately. ¿ American Geophysical Union 1996