In addition to effects from greenhouse gases, climate change is affected by short-lived climate forcers (SLCF). These are often co-emitted with carbon dioxide, and some are regulated air pollutants. In the governance of these pollutants, established estimates of damage costs of pollution inform benefit–cost analyses. However, climate change impact of SLCFs is omitted from these estimates. The purpose of this study is to calculate economic damage costs of air pollutants’ effect on climate change and compare these with established damage costs. Focus is on European emissions governed in the EU National Emission Reduction Commitments Directive during 2020–2050. We use well-known SLCF emission metrics and multiply with literature values on social costs of methane to calculate climate damage costs of SLCFs. The results indicate that average absolute climate damage costs are highest for black carbon ($59,500/ton in 2050) and lowest for nonmethane volatile organic compounds ($661/ton). Our indicative values are likely underestimations. Indicative climate damage costs are usually lower than established damage costs, with notable exceptions. We propose that more detailed studies are necessary, and that inclusion of climate damage costs into economic valuation of SLCFs is important for future air pollution and climate benefit–cost analyses.