Approaches for using diffusion Monte Carlo (DMC) to evaluate matrix elements involving two vibrational wave functions are explored. In the first part of this study, overlaps between a wave function obtained using DMC and one that can be calculated analytically are evaluated. In this case, the analytical wave function is used as the guiding function for an importance sampled DMC simulation. The accuracy of the calculated overlaps is found to depend strongly on the accuracy of the calculated descendant weights, which are obtained in the DMC simulation. While a single evaluation of the descendant weights is sufficient for obtaining projected probability amplitudes or expectation values of multiplicative operators, averages of multiple independent evaluations of the descendant weights are required to obtain accurate matrix elements. This approach is investigated for one-dimensional model systems as well as H2CO, H2D+, and D2H+. The approach is extended to the evaluation of matrix elements of the dipole moment operator between the ground state and states with one quantum of excitation in one of the OH stretching vibrations in H3O2-. For these calculations, the wave functions for both the ground and excited states are evaluated using DMC. The described methodology opens the possibility of evaluating matrix elements involving two different states, both of which are obtained using DMC.