Materials with nanometric dimensions exhibit higher electrical resistivity due to additional scattering centers for the conduction electrons, mainly from surfaces and grain boundaries. In this study we focus on the effect of surfaces by implementing an experimental technique in which the resistivity of thin films is measured during and after etching them inside a solution. This technique enables to analyze the contribution of surfaces to the resistivity and gives a unique insight as for the effect of surface roughness. It is shown that the scattering of electrons from annealed copper films with smooth enough surfaces is mostly specular and that the resistivity in this case is dominated by the effect of grain boundaries. However, when the roughness of the surface becomes larger than the de Broglie wavelength of the electrons, a substantial increase in resistivity occurs. This roughness-induced resistivity is analyzed and shown to be much larger in certain cases than the resistivity predicted for a flat surface, even when all electron scatterings are assumed to be completely diffused.