Supporting Medicaid in the U.S. Territories Act of 2021 This bill extends, increases, and otherwise modifies Medicaid funding for U.S. territories. Specifically, the bill extends (1) the temporarily increased Federal Medical Assistance Percentage (i.e., federal matching rate), and (2) a higher cap on Medicaid funding. Such provisions apply to Puerto Rico through FY2026 and to other territories through FY2029. The bill also requires Puerto Rico to implement an asset verification program and to report on its ability to comply with certain reporting requirements, procurement standards, and other Medicaid program integrity measures.