This paper describes robust vector-fitting algorithms for determining the Q-factor and resonant
frequency of spectrally-isolated resonances from frequency-swept S-parameter measurements for both
one-port (reflection) and two-port (transmission) systems. It also provides guidance on measurement
techniques, and gives measurement examples from the electromagnetic and acoustic domains. These include
measurements on a LC resonator (unloaded Q-factor Qo ≈ 57), a photonic-crystal resonator (Qo ≈ 123 000)
and a superconducting notch resonator (Qo ≈ 1.5 × 106
). The vector techniques advocated are often
advantageous compared to scalar techniques because they are more informative, and in many cases more
precise. Among the most common applications is the measurement of dielectric permittivity and loss by
resonance at RF and microwave frequencies by using Vector Network Analysers. The algorithms described,
however, are applicable more generally to sensing and imaging applications that use vector instrumentation.
This is demonstrated by one of the measurement examples, which shows that acoustic Q-factor can be fitted
to vibrational data obtained by Resonant Ultrasound Spectroscopy. Open-source software implementations
(Python and Matlab) of the algorithms have been made available.