The first practical calculations using two new operators specifically designed for determination of electronic spin and charge density at nuclei are reported. Applications are given for hydrogen, first-row atoms, and first-row diatomic hydrides. Numerical grid methods that simulate complete basis set results confirm a number of relations previously derived formally for the new operators. They also serve as benchmarks for testing the practical utility of the new operators in calculations with small to large Gaussian basis sets. In this connection, the new operators are generally found to have performance superior to the usual delta function formulation and to an alternative one based on the Hiller-Sucher-Feinberg identity.