Offshore well elevation systems often present limit cycles caused by oil-gas slugging. The latest works in control solutions use models based on simple Ordinary Differential Equations to suppress slug flow and increase overall production. However, obtaining parameters for these models is not straightforward due to the occurrence of Hopf bifurcations. Therefore, this work aims to propose a novel methodology to improve parameter estimation. The limit cycle readings of pressure instruments are condensed into a single characteristic cycle with mean value and variance for each sample. Each iteration then uses a modified weighted sum of least squares. This creates a more convex region around the optimum that improves the performance of optimization algorithms. The results were obtained using previously published data for two models. Using the F-test, it was statistically proven that the parameters obtained from the proposed method provided an equivalent or better model fit by employing strictly numeric methods. (C) 2018 Elsevier Ltd. All rights reserved.