We investigate the accuracy of the two-dimensional Finite-Difference Time-Domain (FDTD) method in modelling Surface Plasmon Polaritons (SPPs) in the case of a single metal-dielectric interface and of a thin metal film showing that FDTD has difficulties in the low-group-velocity region of the SPP. We combine a contour-path approach with Z transform to handle both the electromagnetic boundary conditions at the interface and the negative dispersive dielectric function of the metal. The relative error is thus significantly reduced.