We have constructed a sample of 386 radio-loud quasars with z<0.75 from the Sloan Digital Sky Survey in order to investigate orientation effects on black hole mass estimates. Orientation is estimated using radio core dominance measurements based on FIRST survey maps. Black hole masses are estimated from virial-based scaling relationships using H{beta}, and compared to the stellar velocity dispersion ({sigma}*), predicted using the full width at half maximum (FWHM) of [OIII] {lambda}5007, which tracks mass via the M-{sigma}* relation. We find that the FWHM of H{beta} correlates significantly with radio core dominance and biases black hole mass determinations that use it, but that this is not the case for {sigma}* based on [OIII] {lambda}5007. The ratio of black hole masses predicted using orientation-biased and unbiased estimates, which can be determined for radio-quiet as well as radio-loud quasars, is significantly correlated with radio core dominance. Although there is significant scatter, this mass ratio calculated in this way may in fact serve as an orientation estimator. We additionally note the existence of a small population of radio core-dominated quasars with extremely broad H{beta} emission lines that we hypothesize may represent recent black hole mergers.