Catenary damping has long been a tuning parameter in pantograph-catenary dynamic interaction models. As the computed contact force is highly sensitive to the choice of damping model or coefficients, it became critical to measure it independently of the pantograph. Original tests have been conducted on a real catenary and damping identification shows a very low level of damping for a large frequency range. A fitted Rayleigh model and a combined modal and Rayleigh model are proposed and compared with a reference damping model found in literature as well as with the tests. Finally, the consequences on a typical contact force simulation are analysed and the most relevant model is chosen