There is scientific consensus that limiting warming in line with the Paris Agreement goals requires reaching net zero CO2 emissions by mid-century and net negative emissions thereafter. Because of the entrenchment of current fossil fuel energy and feedstock demand estimated in almost all global modelled scenarios, 'abated' fossil fuel and industrial process and product use (IPPU) CO2 emissions, using carbon capture and storage (CCS) technologies to perform carbon management, are likely to be part of any transition. In addition to fossil fuel combustion, this will be primarily in cement & lime kilns, chemical production, and possibly waste incineration and iron and steel making, in processes producing maximally concentrated CO2 waste streams. Abated fossil fuel and IPPU CO2 emissions in the context of recent commitments, however, requires consideration of capture rates for fuel processing and end-use, permanence of storage, reduction of upstream production and end-use fugitive methane, and sufficient means to sequester residual emissions. Based on an assessment of evolving CCS technologies in existing sectors and jurisdictions, criteria are proposed for defining a benchmark for 'abated' fossil fuel and IPPU emissions as where near 100 % GHG abatement is to be eventually achieved, with N2O and fluorinated gases considered separately. This can be accomplished through: 1) CO2 capture rates of more than or equal to 95 % of CO2 emitted; 2) permanent storage of captured emissions; 3) reducing upstream and end-use fugitive methane emissions to <0.5 % and towards 0.2 % of gas production & an equivalent for coal; and 4) counterbalancing remaining emissions using permanent carbon dioxide removal. Application of these criteria to just steel and cement yields estimates of more than or equal to 1.37 Gt CO2 per year reductions after all other reasonable and lower cost actions are taken. At the same time, we acknowledge the value of capture rates below 95 %, so as long they are designed to enable eventual full abatement through process learning. We also discuss commercialisation and deployment policy for CCS, highlighting the need to integrate these criteria into international climate agreements.