Inelastic neutron scattering measurements on monoclinic zirconia $({\mathrm{ZrO}}_{\text{2}})$ and 8 mol% yttrium-stabilized zirconia were performed at temperatures from 300 to $1373w\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. Temperature-dependent phonon densities of states (DOS) are reported, as are Raman spectra obtained at elevated temperatures. First-principles lattice dynamics calculations with density functional theory gave total and partial phonon DOS curves and mode Gr\"uneisen parameters. These mode Gr\"uneisen parameters were used to predict the experimental temperature dependence of the phonon DOS with partial success. However, substantial anharmonicity was found at elevated temperatures, especially for phonon modes dominated by the motions of oxygen atoms. Yttrium-stabilized zirconia (YSZ) was somewhat more anharmonic and had a broader phonon spectrum at low temperatures, owing in part to defects in its structure. YSZ also has a larger vibrational entropy than monoclinic zirconia.