  The most reliable single-epoch supermassive black hole mass ($M_{\rm BH}$)
estimates in quasars are obtained by using the velocity widths of
low-ionization emission lines, typically the H$\beta$ $\lambda4861$ line.
Unfortunately, this line is redshifted out of the optical band at $z\approx1$,
leaving $M_{\rm BH}$ estimates to rely on proxy rest-frame ultraviolet (UV)
emission lines, such as C IV $\lambda1549$ or Mg II $\lambda2800$, which
contain intrinsic challenges when measuring, resulting in uncertain $M_{\rm
BH}$ estimates. In this work, we aim at correcting $M_{\rm BH}$ estimates
derived from the C IV and Mg II emission lines based on estimates derived from
the H$\beta$ emission line. We find that employing the equivalent width of C IV
in deriving $M_{\rm BH}$ estimates based on Mg II and C IV provides values that
are closest to those obtained from H$\beta$. We also provide prescriptions to
estimate $M_{\rm BH}$ values when only C IV, only Mg II, and both C IV and Mg
II are measurable. We find that utilizing both emission lines, where available,
reduces the scatter of UV-based $M_{\rm BH}$ estimates by $\sim15\%$ when
compared to previous studies. Lastly, we discuss the potential of our
prescriptions to provide more accurate and precise estimates of $M_{\rm BH}$
given a much larger sample of quasars at $3.20 \lesssim z \lesssim 3.50$, where
both Mg II and H$\beta$ can be measured in the same near-infrared spectrum.
