Securing And Fortifying Everyday Biomedical Research Act or the SAFE Biomedical Research Act This bill requires the National Institutes of Health (NIH) to address national security concerns with respect to the biomedical research it conducts or supports. Specifically, the NIH must consult with relevant agencies within the Department of Health and Human Services and other federal partners, including the Federal Bureau of Investigation, regarding research that may affect or be affected by matters of national security. The NIH must also ensure that recipients of its funding adhere to appropriate technology practices and policies to safeguard identifiable, sensitive information.