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Objectives. To estimate inequalities in demand for family planning satisfied with modern methods among women in Latin America and the Caribbean, with an emphasis on Brazil and Mexico, and to calculate the scenario for recovery of modern contraceptive coverage by expanding access to long-acting contraceptives (LARC) after the COVID-19 pandemic. Methods. National health surveys from 2006 to 2018 were used to estimate the demand for family planning satisfied with modern methods and how it was affected by the COVID-19 pandemic. The scenario included three variables: coverage, health outcomes, and costs. Considering coverage, United Nations Population Fund data were used to estimate the impact of COVID-19 on access to contraception in Latin America and the Caribbean. Health outcomes were assessed with the Impact 2 tool. Direct investment was used to evaluate cost-effectiveness. Results. Substantial inequalities were found in the use of modern contraceptive methods before the pandemic. We showed the potential cost-effectiveness of avoiding maternal deaths by introducing LARCs. Conclusions. In the scenario predicted for Brazil and Mexico, the costs of modern family planning and averted disability-adjusted life years are modest. Governments in Latin America and the Caribbean should consider promoting LARCs as a highly efficient and cost-effective intervention. [ABSTRACT FROM AUTHOR]