Central banks are increasingly concerned about climate-related risks and want to ensure that the financial system is resilient to them. As they integrate these risks into financial stability monitoring, they also discuss how to apply environmental criteria to their own policy portfolio management, without compromising their policy mandate. We describe different strategies and assess their relevance for central banks, using the Swiss National Bank's (SNB) equity portfolio as a laboratory. We develop a carbon-conscious screening approach that is likely consistent with its policy mandate. The approach reduces the portfolio's carbon footprint by 20%, with little impact on diversification or performance. Received January 26, 2022; editorial decision March 5, 2023 by Editor Andrew Ellul