  The scattering of electromagnetic waves from obstacles with wave-material
interaction in thin layers on the surface is described by generalized impedance
boundary conditions, which provide effective approximate models. In particular,
this includes a thin coating around a perfect conductor and the skin effect of
a highly conducting material. The approach taken in this work is to derive,
analyse and discretize a system of time-dependent boundary integral equations
that determines the tangential traces of the scattered electric and magnetic
fields. In a familiar second step, the fields are evaluated in the exterior
domain by a representation formula, which uses the time-dependent potential
operators of Maxwell's equations. The time-dependent boundary integral
equationis discretized with Runge--Kutta based convolution quadrature in time
and Raviart--Thomas boundary elements in space. Using the frequency-explicit
bounds from the well-posedness analysis given here together with known
approximation properties of the numerical methods, the full discretization is
proved to be stable and convergent, with explicitly given rates in the case of
sufficient regularity. Taking the same Runge--Kutta based convolution
quadrature for discretizing the time-dependent representation formulas, the
optimal order of convergence is obtained away from the scattering boundary,
whereas an order reduction occurs close to the boundary. The theoretical
results are illustrated by numerical experiments.
