Metal films with arrays of subwavelength holes (mesh) exhibit extraordinary transmission resonances to which many attribute a role for surface plasmon polaritons (SPPs); others debated this point. Experimental measurements of propagation lengths are presented under conditions that pertain to the use of SPPs for surface spectroscopy. The lateral extent of electromagnetic propagation along the mesh surface is measured by recording absorption spectra of a line of latex microspheres as a function of distance away from the line along the mesh. Measurements reveal an exponential functional form for decay of absorption signal laterally from the absorption source. Results at 697 cm(-1), which are closest to the strongest transmission resonance of the mesh, reveal a 1/e propagation distance along the surface of 17.8+/-2.9 microm. This is 40% larger than the lattice spacing implicating the holes as the SPP damping mechanism, however, this is significantly shorter than smooth metal expectations.