We present measurements of broad emission lines and virial estimates of supermassive black hole masses (M_BH_) for a large sample of ultrahard 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 of 689 AGNs, determined from the H{alpha}, H{beta}, MgII{lambda}2798, and/or CIV{lambda}1549 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 MBH 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_H_/cm^-2^)>22.0) are on average a factor of 8.0_-2.4_^+4.1^ weaker relative to ultrahard X-ray emission and about 35_-12_^+7^% narrower than those in unobscured sources (i.e., log(N_H_/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 (>1dex) masses for Type 1.9 sources (AGNs with broad H{alpha} but no broad H{beta}) and/or sources with log(N_H_/cm^-2^)>~22.0. We provide simple multiplicative corrections for the observed luminosity and width of the broad H{alpha} component (L[bH{alpha}] and FWHM[bH{alpha}]) in such sources to account for this effect and to (partially) remedy MBH estimates for Type 1.9 objects. As a key ingredient of BASS/DR2, our work provides the community with the data needed to further study powerful AGNs in the low-redshift universe.