A new method (IGAIM - individual gauges for atoms in molecules) is presented for relatively accurate ab initio calculations of molecular magnetic response properties. The current density induced within an atom in a molecule by an external magnetic field is well described by the coupled, perturbed Hartree-Fock method when the gauge origin of the vector potential is placed at its nucleus, the natural origin for the free atom, even though it may be poorly described in the rest of the molecule. Since the molecular magnetic susceptibility and nuclear magnetic shielding tensors can be expressed in terms of the induced current density as a sum of separately determined atomic contributions, these properties are, in general, accurately predicted even with basis sets that are insufficient for conventional CPHF.