This paper presents Far-Ultraviolet Spectroscopic Explorer (FUSE) medium-resolution slit and Chandra X-Ray Observatory ACIS-S observations of the high-excitation planetary nebula NGC 246. The Ne V λ1146 and [Ne V] λ3426 emission lines, the latter obtained in a previous investigation, indicate that the nebula is photoionized by the intense UV radiation of the central object and has a temperature of ~20,000 K. The O VI λ1032 and λ1037 emission lines are moderately optically thick and probably contain contributions from both collisional excitation and radiative scattering of the UV continuum of the central star. The Chandra observation did not detect any X-ray emission from the nebula, but did detect the central star. The absence of nebular X-ray emission and the photoionized nature of the nebula support the hypothesis that the nebula contains a biconical cavity, which extends to the edge of the nebula. In this geometry the stellar wind does not shock the nebular material, resulting only in a cool photoionized plasma. The X-ray spectrum of the central object is consistent with NLTE models for PG 1159-type stars.