Synchronizing the local oscillators in multibeam satellites with the objective of coherent communications is still an open challenge. It has to be addressed to implement full-frequency reuse approaches, such as precoding techniques using the already deployed multibeam satellites. This article addresses the required phase synchronization to enable precoding techniques in multibeam satellite systems. It contains the detailed design of a frequency and phase compensation loop based on the proportional-integral controller, which deals with the phase drift introduced by the hardware components. Specifically, the phase noise of the local oscillators used for up and down conversion at each system element (gateway, satellite, and user terminals). The implementation of the two-state phase noise model used to emulate this phase drift is included in the article. Besides, a comparative analysis of several methods to combine the frequency and phase measurements obtained from the user terminals is also included. Finally, the performance of the proposed closed-loop synchronization method is validated through simulations using our in-house developed MIMO end-to-end satellite emulator based on SDR platforms.