Conger is past Chairman of the World Gold Council; past Chairman of the American Mining Congress; 1994 recipient of the American Mining Congress Distinguished Service Award; a distinguished member of the American Institute of Mining Engineers and the Mining and Metallurgical Society of America; member of the National Academy of Engineering; and recipient of the American Institute of Mining, Metallurgical & Petroleum Engineers' 1990 Charles F. Rand Memorial Award. He was awarded a Distinguished Achievement Medal and Honorary Doctorate by his alma mater, the Colorado School of Mines, and received an Honorary Doctorate degree from the South Dakota School of Mining and Technology. Conger is a Trustee of Caltech.