Energy eigenvalues of the Schrodinger equation for the confined Morse potential are obtained through the variational method and Supersymmetric Quantum Mechanics. Results for the hydrogen molecule are presented to illustrate the procedure. The confinement used here implies that the minimum of the potential is centralized in the confinement region. To obtain this type of confinement two constraints are imposed, the usual confinement radius and a minimum radius. Results are obtained for different values of energy levels, potential parameters and confinement radius. Eigenvalues for the confined harmonic potential are compared with the eigenvalues obtained for the Morse potential. (C) 2010 Elsevier B. V. All rights reserved.