  Model order reduction methods are a powerful tool to drastically reduce the
computational effort of problems which need to be evaluated repeatedly, i.e.,
when computing the same system for various parameter values. When applying a
reduced basis approximation algorithm to the Maxwell eigenvalue problem, we
encounter spurious solutions in the reduced system which hence need to be
removed during the basis construction. In this paper, we discuss two
tree-cotree gauge-based methods for the removal of the spurious eigenmodes.
