Living Shorelines Act This bill directs the National Oceanic and Atmospheric Administration (NOAA) to establish grant programs to support living shoreline projects and research on nature-based infrastructure. NOAA must award grants to state or local governments, nonprofit organizations, and Indian tribes to (1) implement climate-resilient living shoreline projects; and (2) encourage innovation in the use of natural materials to protect coastal communities, habitats, and natural system functions. NOAA shall establish an engineering standard applicable to living shoreline projects for each region of the United States and use such standard to select eligible entities to receive such grants. A grant to carry out a living shoreline project may be used only to carry out the project, including administration, design, permitting, entry into negotiated indirect cost rate agreements, and construction; monitor, collect, and report data on the performance of the project, in accordance with the engineering standard; or incentivize landowners to engage in such projects. NOAA shall award competitive research grants to eligible entities, including U.S. territories, to carry out projects focused on developing and assessing the effectiveness of innovative approaches to nature-based infrastructure for specified climate-related purposes. NOAA shall award grants to such entities for projects that focus on, among other things assessing the effectiveness of installed nature-based infrastructure, or novel approaches to nature-based infrastructure and living shorelines.