We present a method for assimilating total column CH4 : CO2 ratio measurements from satellites for inverse modeling of CH4 and CO2 fluxes using the variational approach. Unlike conventional approaches, in which retrieved CH4 : CO2 are multiplied by model-derived total column CO2 and only the resulting CH4 is assimilated, our method assimilates the ratio of CH4 and CO2 directly and is therefore called the ratio method. It is a dual tracer inversion, in which surface fluxes of CH4 and CO2 are optimized simultaneously. The optimization of CO2 fluxes turns the hard constraint of prescribing model-derived CO2 fields into a weak constraint on CO2, which allows us to account for uncertainties in CO2. The method has been successfully tested in a synthetic inversion setup. We show that the ratio method is able to reproduce assumed true CH4 and CO2 fluxes starting from a prior, which is derived by perturbing the true fluxes randomly. We compare the performance of the ratio method with that of the traditional proxy approach and the use of only surface measurements for estimating CH4 fluxes. Our results confirm that the optimized CH4 fluxes are sensitive to the treatment of CO2, and that hard constraints on CO2 may significantly compromise results that are obtained for CH4. We find that the relative performance of ratio and proxy methods have a regional dependence. The ratio method performs better than the proxy method in regions where the CO2 fluxes are most uncertain. However, both ratio and proxy methods perform better than the surface-measurement-only inversion, confirming the potential of spaceborne measurements for accurately determining fluxes of CH4 and other greenhouse gases (GHGs).