The currently favored method for estimating radii and other parameters of transiting-planet host stars is to match theoretical models to observations of the stellar mean density ρ_*, the effective temperature T _eff, and the composition parameter [Z]. This explicitly model-dependent approach is based on readily available observations, and results in small formal errors. Its performance will be central to the reliability of results from ground-based transit surveys such as TrES, HAT, and SuperWASP, as well as to the space-borne missions MOST, CoRoT, and Kepler. Here, I use two calibration samples of stars (eclipsing binaries (EBs) and stars for which asteroseismic analyses are available) having well-determined masses and radii to estimate the accuracy and systematic errors inherent in the ρ_* method. When matching to the Yonsei-Yale stellar evolution models, I find the most important systematic error results from selection bias favoring rapidly rotating (hence probably magnetically active) stars among the EB sample. If unaccounted for, this bias leads to a mass-dependent underestimate of stellar radii by as much as 4% for stars of 0.4 M _☉, decreasing to zero for masses above about 1.4 M _☉. Relative errors in estimated stellar masses are three times larger than those in radii. The asteroseismic sample suggests (albeit with significant uncertainty) that systematic errors are small for slowly rotating, inactive stars. Systematic errors arising from failings of the Yonsei-Yale models of inactive stars probably exist, but are difficult to assess because of the small number of well-characterized comparison stars having low mass and slow rotation. Poor information about [Z] is an important source of random error, and may be a minor source of systematic error as well. With suitable corrections for rotation, it is likely that systematic errors in the ρ_* method can be comparable to or smaller than the random errors, yielding radii that are accurate to about 2% for most stars.