Methane is the second most important anthropogenic greenhouse gas causing warming after carbon dioxide, and the emission reductions potentials are known to be limited due to the difficulty of abating agricultural methane. We explore in this study the emerging option of atmospheric methane removal (MR) that could complement carbon dioxide removal (CDR) in mitigation pathways. MR is technologically very challenging and potentially very expensive, so the main question is at which cost per ton of methane removed is MR more cost effective than CDR. To address this question, we use an intertemporal optimization climate-GHG-energy model to evaluate the MR cost and removal potential thresholds that would allow us to meet a given climate target with the same or a lower abatement cost and allowing for equal or higher gross CO2 emissions than if CDR through BECCS were an option. We also compare the effects of MR and CDR on the cost-effective mitigation pathways achieving four different climate targets. Using the ACC2-GET integrated carbon cycle, atmospheric chemistry, climate and energy system model, we consider a generic MR technology characterized by a given unit cost and a maximal removal potential. We show that to totally replace bioenergy based CDR with MR, the MR potential should reach at least 180 to 320 MtCH4 per year, i.e., between 50% and 90% of current anthropogenic methane emissions, with maximum unit cost between 10,000 and 34,000 $/tCH4, depending on the climate target. Finally, we found that replacing CDR by MR reshapes the intergenerational distribution of climate mitigation efforts by delaying further the mitigation burden.