The Montreal Protocol has evolved from focusing primarily on ozone layer protection to addressing climate change mitigation, particularly with the 2016 Kigali Amendment establishing a framework for reducing global hydrofluorocarbon (HFC) use. This shift presents an opportunity to link the HFC phasedown with deployment of energy-efficient cooling equipment and thus provide benefits in terms of greenhouse gas reductions, technical and economic synergies, and reduced dumping of environmentally harmful products in developing countries. Although energy-efficiency and refrigerant considerations are still separate in most regions and under most regulatory systems, multilateral agencies can work to couple the financial assistance provided by the Multilateral Fund to Article 5 countries for refrigerant transition under the Montreal Protocol with finance to improve cooling equipment efficiency. In this perspective, we recommend a global governance architecture for the simultaneous transition to efficient cooling equipment and refrigerants with low global warming potential. Our recommendations leverage decades of experience from national energy-efficiency programs along with the Montreal Protocol's refrigerant assistance program. Major elements of the recommended energy-efficiency governance architecture include an internationally harmonized energy-efficiency standards program, product certification and registration, infrastructure for testing energy-efficiency performance, and an evaluation, measurement, and verification strategy. The goal is to optimize investments by national, regional, and international communities that are establishing or improving energy-efficiency standards and compliance infrastructures in tandem with the refrigerant transition. Ultimately, these efforts should help unlock the potential for climate change mitigation under the Kigali Amendment through harmonization of domestic practices and international obligations.