An improved local minimax method (LMM) has been adopted for the calculation of sign-changing solutions for a class of singularly perturbed Semilinear Elliptic Neumann problems. On the one hand, the variable sign-changing solutions of the model problem with different nonlinear terms and domains can be achieved in the ascending order of Morse indices. On the other hand, the energy and maximum value of the same class of variable number solution of the model problem are changing in line with the variation of the singular perturbation parameter. It can be strictly proved that the maximum value of the sign-changing solution is characterized with nonuniform boundedness with respect to the singularly perturbed parameter, with the Morse index of the sign-changing solution equal to or greater than 2 under certain conditions. Based on extensive numerical experiments, a conjecture has thus been proposed about the energy and maximum for the same kind of sign-changing solutions.