  Precise microwave measurements of sample conductivity, dielectric, and
magnetic properties are routinely performed with cavity perturbation
measurements. These methods require the accurate determination of quality
factor and resonant frequency of microwave resonators. Seven different methods
to determine the resonant frequency and quality factor from complex
transmission coefficient data are discussed and compared to find which is most
accurate and precise when tested using identical data. We find that the
nonlinear least-squares fit to the phase vs. frequency is the most accurate and
precise when the signal-to-noise ratio is greater than 65. For noisier data,
the nonlinear least squares fit to a Lorentzian curve is more accurate and
precise. The results are general and can be applied to the analysis of many
kinds of resonant phenomena.
