The numerical lower/upper bound approximation of Maxwell eigenvalues is a very significant but difficult task in scientific and engineering computation. It is a new finding that different convergence orders in L2-norm and H(curl)-semi-norm in spectral element methods would lead to numerical lower/upper bounds of Maxwell eigenvalues. In this paper we study a family of quadrilateral spectral element methods which are characterized by different convergence orders in L2-norm and H(curl)-semi-norm. We prove the optimal L2-norm and H(curl)-semi-norm errors of the spectral element projection. The lower/upper bounds of eigenvalues can be obtained by three spectral element methods with different polynomial degrees. Exponential convergence under p-version refinement are illustrated by computing the eigenvalues with analytic eigenfunction. The lower bounds of eigenvalues with non-smooth eigenfunctions are also observed under p-version refinement. The spectral element methods and the associated results can be extended to three dimension case.