We investigate dielectric saturation and increment in polar liquids under external fields. We couple a previously introduced dipolar solvent model to a uniform electric field and derive the electrostatic kernel of interacting dipoles. This procedure allows an unambiguous definition of the liquid dielectric permittivity embodying non-linear dielectric response and correlation effects. We find that the presence of the external field results in a dielectric anisotropy characterized by a two-component dielectric permittivity tensor. The increase of the electric field amplifies the permittivity component parallel to the field direction, i.e. dielectric increment is observed along the field. However, the perpendicular component is lowered below the physiological permittivity εu ≈ 77, indicating dielectric saturation perpendicular to the field. By comparison with Molecular Dynamics simulations from the literature, we show that the mean-field level dielectric response theory underestimates dielectric saturation. The inclusion of dipolar correlations at the weak-coupling level intensify the mean-field level dielectric saturation and improves the agreement with simulation data at weak electric fields. The correlation-corrected theory predicts as well the presence of a metastable configuration corresponding to the antiparallel alignment of dipoles with the field. This prediction can be verified by solvent-explicit simulations where solvent molecules are expected to be trapped transiently in this metastable state.