Objective: Respiratory sinus arrhythmia (RSA) refers to heart rate oscillations synchronous with respiration, and it is one of the major representations of cardiorespiratory coupling. Its strength has been suggested as a biomarker to monitor different conditions, and diseases. Some approaches have been proposed to quantify the RSA, but it is unclear which one performs best in specific scenarios. The main objective of this study is to compare seven state-of-the-art methods for RSA quantification using data generated with a model proposed to simulate, and control the RSA. These methods are also compared, and evaluated on a real-life application, for their ability to capture changes in cardiorespiratory coupling during sleep. Methods: A simulation model is used to create a dataset of heart rate variability, and respiratory signals with controlled RSA, which is used to compare the RSA estimation approaches. To compare the methods objectively in real-life applications, regression models trained on the simulated data are used to map the estimates to the same measurement scale. Results, and conclusion: RSA estimates based on cross entropy, time-frequency coherence, and subspace projections showed the best performance on simulated data. In addition, these estimates captured the expected trends in the changes in cardiorespiratory coupling during sleep similarly. Significance: An objective comparison of methods for RSA quantification is presented to guide future analyses. Also, the proposed simulation model can be used to compare existing, and newly proposed RSA estimates. It is freely accessible online.