Upgrading from:

NumericalMath`NResidue`

All the functionality of NumericalMath`NResidue` is now available in the newly created Numerical Calculus Package.

To access functionality from the new Numerical Calculus Package, load NumericalCalculus`:

Version 5.2 NumericalMath`NResidue`;
NResidue[1/z, {z, 0}]