  We describe a unified classical approach for analyzing the scattering
coefficients of superconducting microwave resonators with a variety of
geometries. To fill the gap between experiment and theory, we also consider the
influences of small circuit asymmetry and the finite length of the feedlines,
and describe a procedure to correct them in typical measurement results. We
show that, similar to the transmission coefficient of a hanger-type resonator,
the reflection coefficient of a necklace- or bridge-type resonator does also
contain a reference point which can be used to characterize the electrical
properties of a microwave resonator in a single step. Our results provide a
comprehensive understanding of superconducting microwave resonators from the
design concepts to the characterization details.
