As a step towards clarifying the ionization mechanism of LINERs, we have used the Hubble Space Telescope Faint Object Spectrograph to obtain an ultraviolet spectrum of the nucleus of NGC 6500. Compared with more luminous Seyfert nuclei, the emission-line spectrum of NGC 6500 is remarkable for its low-excitation character: C III], C II], and Mg II are the strongest collisionally excited lines in the UV, and C IV is not detected. The fast shock models of Dopita & Sutherland (1995, 1996) are a poor match to the observed spectrum, as they predict much stronger emission than is observed for high-excitation lines such as C IV. Photoionization by an obscured nonstellar continuum source, or possibly ionization by slower (100 km/s) shocks, are more likely explanations for the emission-line ratios. The origin of the UV continuum is unclear; its overall spectral shape is reasonably well matched by spectral evolution models for single-burst populations with ages in the range 70-100 Myr, but no definite absorption features from young stars are present. Alternately, the UV continuum (or some fraction of it) may be scattered radiation from a hidden active nucleus. We tentatively detect a broad He II 4686 emission feature, which may be due to Wolf-Rayet stars, although the UV spectrum does not show any clear Wolf-Rayet signatures. We also find that NGC 6500 is weakly detected in an archival ROSAT HRI image with a luminosity of 5 x 10^40 erg/s in the 0.1-2.4 keV band, within the normal range for LINERs.Comment: 21 pages, 4 figures, LaTeX with AASTeX v4.0 style file, accepted for publication in The Astronomical Journa