The techniques of supersymmetric quantum mechanics are applied to the calculation of the energy difference between the ground state and the first excited state of an asymmetric double well. This splitting, originating from the tunneling effect, is computed via a systematic, rapidly converging perturbation expansion. Perturbative calculations to any order can be easily carried out using a logarithmic perturbation theory. Our approach yield substantially better results than alternative widely used semiclassical analyses.