In 2006, Neri was a recipient of the International Sculpture Center's Lifetime Achievement Award in Contemporary Sculpture. In 2008 he received the Bay Area Treasure Award from the San Francisco Museum of Modern Art. Previous awards include a Guggenheim Foundation Fellowship (1979), National Endowment for the Arts Individual Artist Grant (1980), American Academy and Institute of Arts and Letters Academy-Institute Award in Art (1982), San Francisco Arts Commission Award for Outstanding Achievement in Sculpture (1985), and Orange County Museum of Art Distinguished Artist Award (Newport Beach, CA, 1999). He received Honorary Doctorates from the San Francisco Art Institute (1990), California College of Arts and Crafts (1992), and The Corcoran School of Art, Washington, D.C. (1995).