We calculate the maximum optical absorptance enhancements in thin semiconductor films on metals due to structures that diffuse light and couple it to surface plasmon polaritons. The calculations can be used to estimate plasmonic effects on light-trapping in solar cells. The calculations are based on the statistical distribution of energy in the electromagnetic modes of the structure, which include surface plasmon polariton modes at the metal interface as well as the trapped waveguide modes in the film. The enhancement has the form 4n2+nλ/h (n – film refractive index, λ – optical wavelength, h – film thickness), which is an increase beyond the non-plasmonic “classical” enhancement 4n2. Larger resonant enhancements occur for wavelengths near the surface plasmon frequency; these add up to 2 mA/cm2 to the photocurrent of a solar cell based on a 500 nm film of crystalline silicon. We also calculated the effects of plasmon dissipation in the metal. Dissipation rates typical of silver reverse the resonant enhancement effect for silicon, but a non-resonant enhancement remains.