  This paper describes the calculation of the stationary scattering matrix and
its derivatives for Euclidean waveguides. This is an adaptation and extension
to a procedure developed by Levitin and Strohmaier which was used to compute
the stationary scattering matrix \cite{alexnew}. On Euclidean waveguides, the
scattering matrix can be meromorphically continued from the complex plane to a
Riemann surface with a countably infinite number of sheets. We describe in
detail how we have dealt with this. In addition, our algorithm is also able to
calculate arbitrarily high derivatives. In the final section, we will present
the results of some numerical calculations obtained using this method.
