Wiley was named Best Editorial Cartoonist by the California Newspaper Publishers Association in 1988 and won the Robert F. Kennedy Journalism Award for editorial cartooning in 1991. The National Cartoonists Society honored
Non Sequitur with four awards in the first six years of publication, including their Newspaper Panel Cartoon Award for 1995, 1996 and 1998, and it was nominated for the same award in 1999 and 2002 and won their Newspaper Comic Strip Award for 1992.
Non Sequitur is the only comic strip to win its division during the first year of publication, and it is the only comic feature to win in two divisions, Best Comic Strip for 1992 and Best Newspaper Panel Cartoon for 1995, 1996 and 1998.
- 1988: California Newspaper Publishers Association
- 1991: Robert F. Kennedy Journalism Award, for editorial cartooning
- 1992: National Cartoonists Society, Newspaper Comic Strip Award
- 1995: National Cartoonists Society, Newspaper Panel Cartoon Award
- 1996: National Cartoonists Society, Newspaper Panel Cartoon Award
- 1998: National Cartoonists Society, Newspaper Panel Cartoon Award