We report on results from a target-of-opportunity program to obtain optical spectropolarimetry of flaring $\gamma$-ray blazars with the Southern African Large Telescope (SALT). SALT spectropolarimetry and contemporaneous multi-wavelength spectral energy distributions (SEDs) are modelled self-consistently with a leptonic single-zone model. Such modeling provides an accurate estimate of the degree of order of the magnetic field in the emission region and the thermal contributions from the host galaxy and the accretion disk to the SED, thus putting strong constraints on the physical parameters of the gamma-ray emitting region. For the specific case of the $\gamma$-ray blazar 4C+01.02 ($z = 2.1$), which underwent a large $\gamma$-ray flare in July 2016, we demonstrate that the combined SED and spectropolarimetry modeling provides an estimate of the mass of the central black hole in this blazar to $M_{\rm BH} \sim 2 \times 10^9 \, M_{\odot}$.