We determined the methane (CH4) uptake (at 298 K and 1 to 100 bar pressure) for a variety of covalent organic frameworks (COFs), including both two-dimensional (COF-1, COF-5, COF-6, COF-8 and COF-10) and three-dimensional (COF-102, COF-103, COF-105, COF-108) systems. For all COFs the CH4 uptake was predicted from grand canonical Monte Carlo (GCMC) simulations based on force fiels (FF) developed to fit accurate quantum mechanics (QM) vertical bar second order Moller-Plesset (MP2) perturbation with the equation of state for CH4 and by comparison with the experimental uptake isotherms at 298 K (reported here for COF-5 and COF-8), which agrees well (within 2% for 1 - 100 bar) with the GCMC simulations. From our simulations we have been able to observe, for the first time, multilayer formation coexisting with a pore filling mechanism. The best COF in terms of total volume of CH4 per unit volume COF absorbent is COF-1, which can store 195 v/v at 298 K and 30 bar, exceeding the U.S. Department of Energy target for CH4, storage of 180 v/v at 298 K and 35 bar. The best COFs on a delivery amount basis (volume adsorbed from 5 to 100 bar) are COF-102 and COF-103 with values of 230 and 234 v(STP: 298 K, 1.01 bar)/v, respectively, making these promising materials for practical methane storage.