For characterization of quantum systems measurement data is fitted to various simple models. Examples are an exponential decay for a T1 measurement or a damped sine wave for a T2* measurement. The most common fitting method is ordinary least-squares which ignores the available information on the uncertainty of the measurements.
We analyze different fitting procedures (weighted least-squares and maximum likelihood estimation) in the setting of quantum measurements. We find that the ordinary least-squares is a robust fitting method with excellent performance. The maximum-likelihood framework has value for the interpretation of the validity of the data.