We extend the recently developed converse NMR approach [Thonhauser et al., J. Chem. Phys. 131, 101101 (2009)] such that it can be used in conjunction with norm-conserving, nonlocal pseudopotentials. This extension permits the efficient ab initio calculation of NMR chemical shifts for elements other than hydrogen within the convenience of a plane-wave pseudopotential approach. We have tested our approach on several finite and periodic systems, finding very good agreement with established methods and experimental results.