An electromagnetic cavity as discussed in this contribution will be a source-free region enclosed by a perfect conductor and filled with a linear dielectric in which modes of free oscillation can exist at an infinite number of discrete frequencies. These standing-wave fields and natural frequencies are solutions of the eigenproblem associated with the double-curl operator. If the electric field is the variable solved then the magnetic field will be called the induced field, and vice versa. As is well known, if the operator double-curl is discretized with nodal finite elements then eigenspectrum computed will be severely polluted with spurious eigenmodes, the spurious eigenvalues having the same order of magnitude as the physical eigenvalues and not easily distinguished from them. For an electromagnetic domain discretized by energy-orthogonal finite elements, by a dispersion analysis, the behavior of the induced field energy is researched for the fundamental solution of plane harmonic waves Based on this analysis, for the finite element computation of the cavity eigenspectrum, it is proposed a criterion to efficiently identify the physical eigenmodes between a myriad of spurious eigenmodes.