A method for approximately including quantum effects on the solution to lattice field theories is presented. The formalism is an extension of the semiquantum approximation of Sachrajda, Weldon, and Blankenbecler to obtain lower bounds for quantum Hamiltonians. This approach yields classical-like equations in which the effects of quantum fluctuations is included in a variational manner. The energies obtained by this method should be lower bounds to the true eigenvalues. Vacuum and single-kink solutions are treated in detail, both analytically and numerically.