  We investigate the relationship between the linewidths of broad Mg II
\lambda2800 and Hbeta in active galactic nuclei (AGNs) to refine them as tools
to estimate black hole (BH) masses. We perform a detailed spectral analysis of
a large sample of AGNs at intermediate redshifts selected from the Sloan
Digital Sky Survey, along with a smaller sample of archival ultraviolet spectra
for nearby sources monitored with reverberation mapping. Careful attention is
devoted to accurate spectral decomposition, especially in the treatment of
narrow-line blending and Fe II contamination. We show that, contrary to popular
belief, the velocity width of Mg II tends to be smaller than that of Hbeta,
suggesting that the two species are not cospatial in the broad-line region.
Using these findings and recently updated BH mass measurements from
reverberation mapping, we present a new calibration of the empirical
prescriptions for estimating virial BH masses for AGNs using the broad Mg II
and Hbeta lines. We show that the BH masses derived from our new formalisms
show subtle but important differences compared to some of the mass estimators
currently used in the literature.
