Small Shipyards and Maritime Communities Act This bill revises and reauthorizes through FY2020 the small shipyards program to provide assistance (1) to small shipyards for capital improvements and (2) for maritime training programs to foster technical skills and operational productivity relating to shipbuilding, ship repair, and associated industries. In providing assistance under the program, the U.S. Maritime Administration (MARAD) must take into account the economic circumstances and conditions of maritime communities. Grants may be used for a project only if the steel, iron, and manufactured goods used for the project are produced in the United States, except where MARAD waives such requirements.