Securing America's Medicine Cabinet Act of 2021 This bill directs the Food and Drug Administration (FDA) to designate qualified institutions of higher education (or consortia of such institutions) as National Centers of Excellence in Advanced and Continuous Pharmaceutical Manufacturing and to provide grants to the centers. Each designated center must conduct research on advanced and continuous pharmaceutical manufacturing technologies and must share information from such research with the FDA. (Currently, most drug production involves batch manufacturing, which typically takes longer than continuous manufacturing processes.)