  We study the effects of numerical quadrature rules on error convergence rates
when solving Maxwell-type variational problems via the curl-conforming or edge
finite element method. A complete {\em a priori} error analysis for the case of
bounded polygonal and curved domains with non-homogeneous coefficients is
provided. We detail sufficient conditions with respect to mesh refinement and
precision for the quadrature rules so as to guarantee convergence rates
following that of exact numerical integration. On curved domains, we isolate
the error contribution to numerical quadrature rules.
