Ensemble of inverse modelling estimates of European monthly CH4 fluxes, 0.25 deg. x 0.25 deg, and molar fractions, for 2005-2018 as part of the CoCO2 project and the World Meteorological Organization Integrated Global Greenhouse Gas Information System (WMO-IG3IS). The "Protocol for the intercomparison of national CH4 emissions estimated by inverse modelling systems for Western Europe – Phase 1" by L. Florentie and S. Houweling (https://doi.org/10.5281/zenodo.15082280, 2025) was followed. This dataset is supporting material for Ioannidis, E. et al.: An inter-comparison of inverse models for estimating European CH4 emissions. In preparation. Earth System Science Data Copernicus (to be submitted).