Remote sensing of oceanic and atmospheric quantities,such as the waveheight spectrum and wind velocity, depend largely on the interaction of electromagnetic radar waves with ocean surface waves in the short gravity and capillary range. The propagation of such ripple waves upon the ocean surface is strongly affected by the presence of surface films which constitute the ocean microlayer. In order to understand the impact of surface films on oceanic and atmospheric remote sensing, it is necessary to have an accurate and, if possible, convenient model relating film properties with the propagation and damping of ripple waves. This study examines two different methods of obtaining the damping coefficient of short gravity and capillary waves. One method, developed by Bock and Mann, utilizes numerical techniques based on the modified Levich characteristic equation to accurately yield complex roots governing the propagation of Laplace transverse and Marangoni longitudinal waves on the air-sea interface. The other method, developed by Cini and Lombardini, involves finding an approximate analytical solution of the Levich equations using a perturbational technique. A comparison of the two methods yields tolerance ranges of various parameters, including frequency, modulus of surface dilational viscosity, and modulus of surface dilational elasticity, over which the two methods agree to 5--10%. To make our comparison concrete, we apply both methods to a specific surface film sample collected by Garret. Both theoretical results are compared to experimental results. ¿ American Geophysical Union 1992