  In the first part of the paper a generalized theoretical approach towards
beam coupling impedances and stretched-wire measurements is introduced. Applied
to a circular symmetric setup, this approach allows to estimate the systematic
measurement error due to the presence of the wire. Further, the interaction of
the beam or the TEM wave, respectively, with dispersive material such as
ferrite is discussed. The dependence of the obtained impedances on the
relativistic velocity $\beta$ is investigated and found as material property
dependent. The conversion formulas for the TEM scattering parameters from
measurements to impedances are compared with each other and the analytical
impedance solution. In the second part of the paper the measurements are
compared to numerical simulations of wakefields and scattering parameters. In
practice, the measurements have been performed for the circularly symmetric
example setup. The optimization of the measurement process is discussed. The
paper concludes with a summary of systematic and statistic error sources for
impedance bench measurements and their diminishment strategy.
