The inclusion of electronic polarization within Monte Carlo calculations of simple models of molecular liquids is hampered, relative to its inclusion within molecular dynamics calculations, by the need to fully determine the variables that specify the electronic configuration every time each molecule is moved, i.e., N times per cycle, rather than once per cycle. Classical statistical mechanical Monte Carlo calculations on two models of liquid water have been performed. For each of the models, electronic degrees of freedom are modeled by polarizable sites; thus it is the components of the induced dipole vector that must be determined at each step. Commonly used approximation methods have been characterized and found to be inadequate. Efficient procedures have been devised to estimate the dipole vector and have been tested on reproducing electronic, thermodynamic, and structural properties of the two polarizable water models. The most promising procedure, considering both computational time saved and accuracy at reproducing pure liquid properties, involves approximating the induced dipoles at each step by an initial perturbative modification of the dipoles from the previous step, followed by an iteration of the induced dipoles on only the moved molecule. With this procedure, the CPU time is dramatically reduced, and the thermodynamic and structural properties are estimated correctly to within a few percent. They are reproduced more rapidly and with greater accuracy than in calculations in which the dipole vector is estimated by a single iterative cycle starting with the dipoles from the previous Monte Carlo step.