We present measurements of broad emission lines and virial estimates of supermassive black hole masses (\(M_{BH}\)) for a large sample of ultra-hard X-ray selected active galactic nuclei (AGNs) as part of the second data release of the BAT AGN Spectroscopic Survey (BASS/DR2). Our catalog includes \(M_{BH}\) estimates for a total 689 AGNs, determined from the H\(\alpha\), H\(\beta\), \(MgII\lambda2798\), and/or \(CIV\lambda1549\) broad emission lines. The core sample includes a total of 512 AGNs drawn from the 70-month Swift/BAT all-sky catalog. We also provide measurements for 177 additional AGNs that are drawn from deeper Swift/BAT survey data. We study the links between \(M_{BH}\) estimates and line-of-sight obscuration measured from X-ray spectral analysis. We find that broad H\(\alpha\) emission lines in obscured AGNs (\(\log (N_{\rm H}/{\rm cm}^{-2})> 22.0\)) are on average a factor of \(8.0_{-2.4}^{+4.1}\) weaker, relative to ultra-hard X-ray emission, and about \(35_{-12}^{~+7}\)\% narrower than in unobscured sources (i.e., \(\log (N_{\rm H}/{\rm cm}^{-2}) < 21.5\)). This indicates that the innermost part of the broad-line region is preferentially absorbed. Consequently, current single-epoch \(M_{BH}\) prescriptions result in severely underestimated (\(>\)1 dex) masses for Type 1.9 sources (AGNs with broad H\(\alpha\) but no broad H\(\beta\)) and/or sources with \(\log (N_{\rm H}/{\rm cm}^{-2}) > 22.0\). We provide simple multiplicative corrections for the observed luminosity and width of the broad H\(\alpha\) component (\(L{\rm b}{\rm H}\alpha\) and FWHMbH\(\alpha\)) in such sources to account for this effect, and to (partially) remedy \(M_{BH}\) estimates for Type 1.9 objects. As key ingredient of BASS/DR2, our work provides the community with the data needed to further study powerful AGNs in the low-redshift Universe.