In municipal wastewater treatment plants, some dissolved methane can enter the aerobic bioreactors. This greenhouse gas originates from sewers and return flows from anaerobic sludge treatment. In well-mixed conventional activated sludge reactors, methane emissions are largely avoided because methane oxidizing bacteria consume a large fraction, even without optimizing for this purpose. In this work, the fate of dissolved methane is studied in aerobic granular sludge reactors, as they become increasingly popular. The influence of the characteristic design and operating conditions of these reactors are studied with a mathematical model with apparent conversion kinetics and stripping: the separation of feeding and aeration in time, a higher substrate transport resistance, a high retention time of granular biomass and a taller water column. Even for a best-case scenario combining an unrealistically low intragranule substrate transport resistance, a high retention time, a tall reactor, an extremely high influent methane concentration and no oxygen limitation, the methane conversion efficiency was only 12% when feeding and aeration were separated in time, which is lower than for continuous activated sludge reactors under typical conditions. A more rigorous model was used to confirm the limited conversion, considering the multi-species and multi-substrate biofilm kinetics, anoxic methane consumers and the high substrate concentration at the bottom during upward plug flow feeding. The observed limited methane conversion is mainly due to the high concentration that accumulates during unaerated feeding phases, which favours stripping more than conversion in the subsequent aeration phase. Based on these findings, strategies were proposed to mitigate methane emissions from wastewater treatment plants with sequentially operated reactors.