The mechanical properties of films of gels composed of a crude oil or corn oil and (R)-12-hydroxystearic acid are described using oscillatory rheology and water-surface waves. The integrity of these gel films are contrasted with those of neat oil films subjected to the same types of mechanical testing. The oil-based gels are thixotropic, and we quantify their post-recovery yield. A simple model is proposed to describe the loss of integrity when the gels are subjected to high amplitude surface waves. Our technique provides a novel method for quantifying the role of dynamic surface perturbations on the mechanics of viscoelastic films, providing an illustrative model system for testing coagulants and dispersants designed to mitigate oil spills.