Tech to Save Moms Act This bill supports the use of technology to address maternal health outcomes. Specifically, the bill permits the Center for Medicare and Medicaid Innovation to test telehealth models to screen and treat common pregnancy-related complications for Medicaid enrollees and establishes two grant programs that leverage technology to address maternal health outcomes. The Department of Health and Human Services must award grants to (1) entities that provide services to pregnant and postpartum women in specified areas, or from certain populations, to evaluate and expand technology-enabled collaborative learning models; and (2) public or private entities, including tribes, to reduce racial and ethnic disparities in maternal health outcomes by increasing access to digital tools. In addition, the National Academies of Sciences, Engineering, and Medicine must study the use of technology to reduce preventable maternal mortality and severe maternal morbidity and racial and ethnic disparities in maternal health outcomes.