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Peer reviewed ; © 2020 by the authors. The use of probability-based panels that collect data via online or mixed-mode surveys has increased in the last few years as an answer to the growing concern with the quality of the data obtained with traditional survey modes. However, in order to adequately represent the general population, these tools must address the same sources of bias that affect other survey-based designs: namely under coverage and non-response. In this work, we test several approaches to produce calibration estimators that are suitable for survey data affected by non response where auxiliary information exists at both the panel level and the population level. The first approach adjusts the results obtained in the cross-sectional survey to the population totals, while, in the second, the weights are the result of two-step process where different adjusts on the sample, panel, and population are done. A simulation on the properties of these estimators is performed. In light of theory and simulation results, we conclude that weighting by calibration is an effective technique for the treatment of non-response bias when the response mechanism is missing at random. These techniques have also been applied to real data from the survey Andalusian Citizen Preferences for Political Decision-Making Procedures. The work was supported by the Ministerio de Economia, Industria y Competitividad, Spain, under Grant MTM2015-63609-R.