  We present an a posteriori estimator of the error in the L^2-norm for the
numerical approximation of the Maxwell's eigenvalue problem by means of
N\'ed\'elec finite elements. Our analysis is based on a Helmholtz decomposition
of the error and on a superconvergence result between the L^2-orthogonal
projection of the exact eigenfunction onto the curl of the N\'ed\'elec finite
element space and the eigenfunction approximation. Reliability of the a
posteriori error estimator is proved up to higher order terms and local
efficiency of the error indicators is shown by using a standard bubble
functions technique. The behavior of the a posteriori error estimator is
illustrated on a numerical test.
