Maritime Transportation System Emergency Relief Act of 2020 This bill authorizes the U.S. Maritime Administration (MARAD) to provide financial assistance to states and maritime industry entities during an emergency such as COVID-19 (i.e., coronavirus disease 2019). Specifically, MARAD may provide grants for operating costs involved with an emergency response operation, including costs for cleaning, sanitizing, janitorial services, staffing, paid leave, and procuring personal protective equipment; and the costs of capital projects to protect, repair, reconstruct, or replace equipment and facilities of the United States maritime transportation system that are in danger of suffering serious damage, or has suffered serious damage, as a result of an emergency. The federal share payable of the costs for which a grant is provided under the bill shall be 100%.