The temperature dependences of the line widths observed in solid-state C-13 NMR spectra for several polymers are shown to correlate with the time and temperature dependences of the segmental dispersions in their dielectric relaxation spectra. The NMR line width variations arise from molecular motions which modulate the H-1-C-13 dipolar interaction and the chemical shift anisotropy (CSA), thus interfering with the proton decoupling of the dipolar interaction and the magic angle spinning modulation of the CSA. These same motions govern the local segmental dynamics, and hence there is a direct connection between the results from macroscopic probes of polymer relaxation such as dielectric spectroscopy and microscopy measurements like NMR. The polymers studied herein exhibit a range of segmental relaxation properties, ranging from narrow relaxation functions with weak temperature dependences to very broad relaxation spectra whose mean relaxation times change markedly with temperature. In the C-13 NMR experiments these behaviors correspond to line broadening over very wide or narrow temperature ranges, respectively Our analysis demonstrates the manner in which solid-state NMR spectroscopy can provide information on the segmental dynamics of polymers, interpretable in the framework of relaxation models.