Primary steelmaking in blast and basic oxygen furnaces is inherently carbon-intensive. Partial capture, i.e., capturing only a share of the CO2, is discussed as an option to reduce the cost of carbon capture and storage (CCS) and to realize a near-term reduction in emissions from the steel industry. This work presents a techno-economic assessment of partial capture based on amine absorption of CO2. The cost of steam from excess heat is assessed in detail. Using this steam to drive the capture process yields costs of 28–50 €/t CO2-captured. Capture of CO2 from the blast furnace gas outperforms end-of-pipe capture from the combined-heat-and-power plant or hot stove flue gases onsite by 3–5 €/t CO2-captured. The study shows that partial capture driven exclusively by excess heat represents a lower cost for a steel mill owner, estimated in the range of 15–30 €/t CO2-captured, as compared to full capture driven by the combustion of extra fuel. In addition, the full-chain CCS cost (capture, transport and storage) for partial capture is discussed in light of future carbon prices. We conclude that implementation of partial capture in the steel industry in the 2020s is possible and economically viable if policymakers ensure long-term regulation of carbon prices in line with agreed emission reduction targets beyond Year 2030.