Using a sample of high-redshift lensed quasars from the CASTLES project with observed-frame ultraviolet or optical and near-infrared spectra, we have searched for possible biases between supermassive black hole (BH) mass estimates based on the CIV, Halpha and Hbeta broad emission lines. Our sample is based upon that of Greene, Peng & Ludwig, expanded with new near-IR spectroscopic observations, consistently analyzed high S/N optical spectra, and consistent continuum luminosity estimates at 5100A. We find that BH mass estimates based on the FWHM of CIV show a systematic offset with respect to those obtained from the line dispersion, sigma_l, of the same emission line, but not with those obtained from the FWHM of Halpha and Hbeta. The magnitude of the offset depends on the treatment of the HeII and FeII emission blended with CIV, but there is little scatter for any fixed measurement prescription. While we otherwise find no systematic offsets between CIV and Balmer line mass estimates, we do find that the residuals between them are strongly correlated with the ratio of the UV and optical continuum luminosities. Removing this dependency reduces the scatter between the UV- and optical-based BH mass estimates by a factor of approximately 2, from roughly 0.35 to 0.18 dex. The dispersion is smallest when comparing the CIV sigma_l mass estimate, after removing the offset from the FWHM estimates, and either Balmer line mass estimate. The correlation with the continuum slope is likely due to a combination of reddening, host contamination and object-dependent SED shapes. When we add additional heterogeneous measurements from the literature, the results are unchanged.