Recent calls advocate that a huge reduction in the consumption of animal products (including dairy) is essential to mitigate climate change and stabilise global warming below the 1.5 and 2°C targets. The Paris Agreement states that to stabilise temperatures we must reach a balance between anthropogenic emissions by sources and removals by sinks of greenhouse gases (GHG) in the second half of this century. Consequently, many countries have adopted overall GHG reduction targets (e.g. EU, at least 40% by 2030 compared to 1990). However, using conventional metric-equivalent emissions (CO2-e GWP100) as the basis to account for emissions does not result in capturing the effect on atmospheric warming of changing emission rates from short-lived GHG (e.g. methane: CH4), which are the main source of GHG emissions by small ruminants. This shortcoming could be solved by using warming-equivalent emissions (CO2-we, GWP*), which can accurately link annual GHG emission rates to its warming effect in the atmosphere. In our study, using this GWP* methodology and different modelling approaches, we first examined the historical (1990–2018) contribution of European dairy small ruminant systems to additional atmosphere warming levels and then studied different emission target scenarios for 2100. These scenarios allow us to envision the necessary reduction of GHG emissions from Europe's dairy small ruminants to achieve a stable impact on global temperatures, i.e. to be climatically neutral. Our analysis showed that, using this type of approach, the whole European sheep and goat dairy sector seems not to have contributed to additional warming in the period 1990–2018. Considering each subsector separately, increases in dairy goat production has led to some level of additional warming into the atmosphere, but these have been compensated by larger emission reductions in the dairy sheep sector. The estimations of warming for future scenarios suggest that to achieve climate neutrality, understood as not adding additional warming to the atmosphere, modest GHG reductions of sheep and goat GHG would be required (e.g. via feed additives). This reduction would be even lower if potential soil organic carbon (SOC) from associated pastures is considered.