Spoof surface modes on nanostructured metallic surfaces are known to have tailorable dispersion dependent on the geometric characteristics of the periodic pattern. Here we examine the spoof plasmon dispersion on an isolated grating and a grating-planar mirror cavity configuration. The spoof polariton dispersion in the cavity is obtained using the scattering matrix approach, and the related differential modal density of states is introduced to obtain the mode dispersion and classify the cavity polariton modes. The grating-mirror cavity geometry is an example of periodically nanostructured metals above a planar ground plane. The properties discussed here are relevant for applications ranging from thin electromagnetic perfect absorbers to near-field radiative heat transfer. ; Comment: 14 pages, 7 figures