Abstract. Methane is a strong greenhouse gas and large uncertainties exist concerning the future evolution of its atmospheric abundance. Analyzing methane atmospheric mixing and stable isotope ratios in air trapped in polar ice sheets helps in reconstructing the evolution of its sources and sinks in the past. This is important to improve predictions of atmospheric CH4 mixing ratios in the future under the influence of a changing climate. The aim of this study is to assess whether past atmospheric δ13C(CH4) variations can be reliably reconstructed from firn air measurements. Isotope reconstructions obtained with a state of the art firn model from different individual sites show unexpectedly large discrepancies and are mutually inconsistent. We show that small changes in the diffusivity profiles at individual sites lead to strong differences in the firn fractionation, which can explain a large part of these discrepancies. Using slightly modified diffusivities for some sites, and neglecting samples for which the firn fractionation signals are strongest, a combined multi-site inversion can be performed, which returns an isotope reconstruction that is consistent with firn data. However, the isotope trends are lower than what has been concluded from Southern Hemisphere (SH) archived air samples and high-accumulation ice core data. We conclude that with the current datasets and understanding of firn air transport, a high precision reconstruction of δ13C of CH4 from firn air samples is not possible, because reconstructed atmospheric trends over the last 50 yr of 0.3–1.5 ‰ are of the same magnitude as inherent uncertainties in the method, which are the firn fractionation correction (up to ~2 ‰ at individual sites), the Kr isobaric interference (up to ~0.8 ‰, system dependent), inter-laboratory calibration offsets (~0.2 ‰) and uncertainties in past CH4 levels (~0.5 ‰).