Protein charge organization is dependent on the low-permittivity region in the hydrophobic core of the molecule. We suggest a novel approach to estimate the dielectric constant of this region by comparing measured and simulated first- and second-order charge moments. Here, the dipole moment is measured as a function of pH using dielectric spectroscopy. The results are compared to dipole moments based on Poisson-Boltzmann estimates of pK(a) shifts calculated from structures in the Protein Data Bank. Structures are additionally refined using CHARMM molecular dynamics simulations. The best estimate for the internal permittivity is found by minimizing the root-mean-square residual between measured and predicted charge moments. Using the protein beta-lactoglobulin, a core dielectric constant in the range of 6-7 is estimated.