The model reduction problem for continuous-time, linear, time-invariant systems is studied at isolated singularities of the transfer function. The moments at a pole of the transfer function are shown to be uniquely specified by the solutions of certain Sylvester equations exploiting two distinct approaches based on complex analysis and on geometric control theory. This allows to determine reduced order models which preserve given poles and match the corresponding moments. An in-depth analysis of the assumptions underlying this approach is provided in a companion paper. The applicability of the approaches developed is demonstrated with simple academic examples.