We describe what may be the most accurate approach currently available for the calculation of the pKas of ionizable groups in proteins. The accuracy is assessed by comparison of computed pKas with 60 measured pKas in a total of seven proteins. The overall root-mean-square error is 0.89 pKa units. Linear regression analysis of computed versus measured pKas yields a slope of 0.95, y-intercept of -0.02 and a correlation coefficient of 0.96. The proposed approach also picks out many of the shifted pKas of groups in enzyme active sites and special salt bridges. However, it does yield several over-shifted pKas and tends to underestimate pKa shifts which result from desolvation effects. We examine the ability of the new approach to reproduce the dependence of protein stability upon pH, using the ionization polynomial formalism. Overall features of the stability curves are reproduced, but the quantitative agreement is not particularly good. The reasons for the disagreement may have to do both with insufficient accuracy in the theory and with uncertainty in the nature of the unfolded state of proteins. The methodology described here is based upon finite difference solutions of the Poisson-Boltzmann equation. Its success depends upon the use of the rather high protein dielectric constant of 20. However, theoretical considerations and the fact that pKa shifts which result from desolvation are underestimated here imply that the dielectric constant of the protein interior actually is lower than 20. We suggest that the high protein dielectric constant improves the overall agreement with experiment because it accounts approximately for phenomena which tend to mitigate pKa shifts and which are not specifically included in the model. These include conformational relaxation and specific ion-binding. Future models based upon a low protein dielectric constant and treating such phenomena explicitly might yield improved agreement with experiment.