The effects of a dielectric medium on the magnetizabilities and nuclear shielding constants of the fluoromethanes are calculated in a gauge-origin independent approach. It is shown that in order to model the effects of a dielectric medium properly, we have to go beyond the dipole approximation and the geometry has to be optimized for each value of the dielectric constant. Geometrical distortions play an important role, as is clearly demonstrated for the magnetizability of the CH3F molecule where the geometrical distortions alter the sign of the dielectric contribution to the solvent shift. The effects on the nuclear shielding constants from a dielectric medium are interpreted in terms of the polarization of the charge distribution and the change in geometry. Other medium effects on nuclear shielding constants are discussed, and it is demonstrated that they must be included in order to reproduce the experimental gas-to-liquid chemical shift of the CH3F and CHF3 molecules. Basis set convergence and electron correlation effects of the magnetizabilities and the nuclear shielding constants in the gas phase are also investigated.