In this work, we consider different waveguide structures comprising a metal and a dispersive negative index material (NIM) which has negative permittivity and permeability over a frequency band in the microwave range of several GHz. In the first structure, one interface separating a semi-infinite metal and a semi-infinite NIM is assumed. In the second structure, a NIM slab is sandwiched between a metal and a dielectric material whereas in the third structure a metal slab is embedded in a NIM medium. The dispersion relations and the conditions for surface polariton excitation at the interfaces are derived, plotted and discussed. Penetration depth and modal refractive index are also studied.