Currently, various satellite processing centers produce extensive data, with different solutions of the same field being available. For instance, the Gravity Recovery and Climate Experiment (GRACE) has been monitoring terrestrial water storage (TWS) since April 2002, while the Center for Space Research (CSR), the Jet Propulsion Laboratory (JPL), the GeoForschungsZentrum (GFZ), and the Groupe de Recherche de Géodésie Spatiale (GRGS) provide individual monthly solutions in the form of Stokes coefficients. The inverted TWS maps (or the regionally averaged values) from these coefficients are being used in many applications; however, as no ground truth data exist, the uncertainties are unknown. Consequently, the purpose of this work is to assess the quality of each processing center by estimating their uncertainties using a generalized formulation of the three-cornered hat (TCH) method. Overall, the TCH results for the study period of August 2002 to June 2014 indicate that at a global scale, the CSR, GFZ, GRGS, and JPL presented uncertainties of 9.4, 13.7, 14.8, and 13.2 mm, respectively. At a basin scale, the overall good performance of the CSR was observed at 91 river basins. The TCH-based results were confirmed by a comparison with an ensemble solution from the four GRACE processing centers.