| Year,Result,Award,Category,Work | |
| 1996,Won,DownBeat Readers Poll,Alto Saxophone,- | |
| 1997,Won,DownBeat Readers Poll,Alto Saxophone,- | |
| 1997,Won,DownBeat Readers Poll,Jazz Album of the Year,Pursuance: The Music of John Coltrane | |
| 1997,Nominated,Grammy Award,Best Jazz Instrumental Performance,Songbook | |
| 1998,Won,DownBeat Readers Poll,Alto Saxophone,- | |
| 1999,Won,DownBeat Readers Poll,Alto Saxophone,- | |
| 2006,Nominated,Grammy Award,Best Jazz Instrumental Album,Beyond the Wall | |
| 2009,Won,DownBeat Readers Poll,Alto Saxophone,- | |
| 2010,Won,DownBeat Readers Poll,Alto Saxophone,- | |
| 2010,Won,Grammy Award,Best Jazz Instrumental Album,Five Peace Band - Live | |
| 2012,Nominated,Grammy Award,Best Jazz Instrumental Album,Seeds from the Underground | |
| 2012,Nominated,Grammy Award,Best Improvised Jazz Solo,"""J. Mac""" | |
| 2012,Nominated,NAACP Image Award,Outstanding Jazz Album,Seeds from the Underground | |
| 2012,Nominated,Soul Train Award,Best Traditional Jazz Artist/Group,Seeds from the Underground | |
| 2012,Nominated,Jazz Awards,Alto Saxophonist of the Year,- | |
| 2012,Won,Echo Award,Saxophonist of the Year,- | |
| 2012,Won,DownBeat Readers Poll,Alto Saxophone,- | |
| 2013,Won,DownBeat Readers Poll,Alto Saxophone,- | |
| 2013,Nominated,Grammy Award,Best Jazz Instrumental Album,Pushing the World Away | |