Safe Drinking Water Assistance Act of 2019 This bill addresses contaminants of emerging concern (emerging contaminants), which are not regulated under a national primary drinking water regulation and may have an adverse effect on human health. The Environmental Protection Agency (EPA) must review federal efforts to (1) identify, monitor, and assist in the development of treatment methods for emerging contaminants; and (2) assist states in responding to the human health risks posed by those contaminants. In addition, the EPA must establish a strategic plan for improving those efforts. The EPA and the Department of Health and Human Services must jointly establish an interagency working group to coordinate federal activities that identify and analyze the public health effects of emerging contaminants. The Office of Science and Technology Policy must establish a National Emerging Contaminant Research Initiative to (1) improve the identification, analysis, monitoring, and treatment methods of emerging contaminants; and (2) support the implementation of its cross-agency plan for addressing research gaps related to detecting, assessing exposure to, and identifying the adverse health effects of such contaminants. Specified federal agencies must make grants for research proposals that are likely to result in significant progress toward achieving the plan's objectives. The EPA must (1) report on actions it may take to increase technical assistance and support for states with respect to emerging contaminants in drinking water samples, and (2) develop a program to provide technical assistance and support to states for the testing and analysis of emerging contaminants.