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Abstract The most reliable single-epoch supermassive black hole mass (M_BH) estimates in quasars are obtained by using the velocity widths of low-ionization emission lines, typically the Hβλ4861 line. Unfortunately, this line is redshifted out of the optical band atz≈ 1, leavingM_BHestimates to rely on proxy rest-frame ultraviolet (UV) emission lines, such as Civλ1549 or Mgiiλ2800, which contain intrinsic challenges when measuring, resulting in uncertainM_BHestimates. In this work, we aim at correctingM_BHestimates derived from the Civand Mgiiemission lines based on estimates derived from the Hβemission line. We find that employing the equivalent width of Civin derivingM_BHestimates based on Mgiiand Civprovides values that are closest to those obtained from Hβ. We also provide prescriptions to estimateM_BHvalues when only Civ, only Mgii, and both Civand Mgiiare measurable. We find that utilizing both emission lines, where available, reduces the scatter of UV-basedM_BHestimates by ∼15% when compared to previous studies. Lastly, we discuss the potential of our prescriptions to provide more accurate and precise estimates ofM_BHgiven a much larger sample of quasars at 3.20 ≲z≲ 3.50, where both Mgiiand Hβcan be measured in the same near-infrared spectrum.