Set Testing and Objectives Plan for COVID-19 Act or the STOP COVID-19 Act This bill establishes two grant programs to support public health measures to address COVID-19 (i.e., coronavirus disease 2019). First, the Department of Health and Human Services (HHS) must award grants to local health departments for testing, contact tracing, and other activities to reduce the spread of COVID-19. A recipient of one of these grants must meet specific standards for testing and contact tracing. If a grantee remains unable to meet those standards after two months, it must return a portion of the grant funding. HHS may use unobligated funds from the Public Health and Social Services Emergency Fund for these grants. The authority to make these grants terminates when that funding is expended or 180 days after this bill's enactment, whichever is earlier. Second, HHS must award grants to support COVID-19 vaccination efforts in states and territories. A recipient of one of these grants must publicly report information about its vaccine efforts, develop a unified system to register its residents for vaccines, and administer at least 95% of its vaccine allotment each month. If a grantee fails to use the required percentage of its vaccines, it must return a portion of the grant funding. HHS may use specified COVID-19 relief funding for these grants. The authority to make these grants terminates when that funding is expended or December 31, 2021, whichever is earlier.