The methane deliverable capacity of adsorbent materials is a critical performance metric that will determine the viability of using adsorbed natural gas (ANG) technology in vehicular applications. ARPA-E recently set a target deliverable capacity of 315 cc(STP)/cc that a viable adsorbent material should achieve to yield a driving range competitive with incumbent fuels. However, recent computational screening of hundreds of thousands of materials suggests that the target is unattainable. In this work, we aim to determine whether the observed limits in deliverable capacity (~200 cc(STP)/cc) are fundamental limits arising from thermodynamic or material design constraints. Our efforts focus on simulating methane adsorption isotherms in a large number of systems, resulting in a broad exploration of different combinations of spatial distributions and energetics of adsorption sites. All systems were classified into five adsorption scenarios with varying degrees of realism in the manner that adsorption sites are created and endowed with energetics. The scenarios range from methane adsorption on discrete idealized lattice sites to adsorption in metal–organic frameworks with coordinatively unsaturated sites (CUS) provided by metalated catechol groups. Our findings strongly suggest that the ARPA-E target is unattainable, although not due to thermodynamic constraints but due to material design constraints. On the other hand, we also find that the currently observed deliverable capacity limits may be moderately surpassed. For instance, incorporation of CUS in IRMOF-10 is predicted to yield a 217 cc(STP)/cc deliverable capacity. The modified material has a ~0.85 void fraction and a heat of adsorption of ~15 kJ/mol. This suggests that similar, moderate improvements over existing materials could be achieved as long as CUS incorporation still maintains a relatively large void fraction. Nonetheless, we conclude that more significant improvements in deliverable capacity will require changes in the currently proposed operation conditions.