Maritime Technological Advancement Act of 2021 This bill authorizes the Maritime Administration to award maritime career training grants to eligible institutions (i.e., postsecondary educational institutions or postsecondary vocational institutions for the purpose of developing, offering, or improving educational or career training programs for American workers in the maritime workforce. Each awarded grant may not exceed $20 million. The Maritime Administration must award grants based on a determination of the merits of the grant proposal submitted by an eligible institution to develop, offer, or improve maritime educational or career training programs; an evaluation of the likely employment opportunities available to workers who complete a maritime educational or career training program; an evaluation of prior demand for training programs by workers, and the availability and capacity of existing maritime training programs to meet future demand for training programs; any prior designation of an eligible institution as a Center of Excellence for Domestic Maritime Workforce Training and Education; and an evaluation of the previous experience of the eligible institution in providing maritime educational or career training programs.