Environmental Stewardship and Natural Resources Act of 1999 - Designates the Idaho National Engineering and Environmental Laboratory as the Center of Excellence of Environmental Stewardship of the Department of Energy (DOE). Cites Center duties, including development, testing, and demonstration of methods and technologies necessary for DOE's long-term stewardship of defense nuclear facility lands affected by legacy waste.

Requires the Center to enter into memoranda of understanding with Federal agencies to establish administrative procedures to: (1) participate in work for other programs on lands of the Departments of the Interior and of Agriculture; and (2) solve pressing long-term stewardship problems.

Establishes a Natural Resources Institute as a pilot demonstration project within the Center to: (1) serve as partner and facilitator in performing enumerated Center duties; (2) perform multidisciplinary research regarding long-term stewardship; (3) support formulation and implementation of long-term stewardship public policy; and (4) act as an information resource center.

Mandates Institute cooperation with governmental agencies, colleges and universities, national laboratories, and with the public.