What are some popular jazz songs that are mostly just trumpet or sax?

um, St. Louis Blues maybe, or The Girl From Ipanema?

Chet Baker Charlie Parker Lester Young Anything past the 1950's I don't know except for Matheny and a few canaries.

thelonious monk and john clotrane-blue monk??

Whirlybird ( Count Basie Band ) My Dad played the tenor Sax solo in there...it's a favorite) Shiny Stockings ( Dad wrote and played the tenor sax in there) Night In Tunisia - ( trumpet solo) By Dizzy Gillespie or Byron Stripling solo wihen he was with the Basie band

David Sanborn Bob James... Maputo?

This is not a good question! Your answers are already all over the place-- especially time era wise! You give us no clue (except that it probably is not Kenny G) as to what era you are talking about. There are literally millions of songs that either feature sax or trumpet. Anything by Spyro Gyra would feature sax in the recent era. Wynton Marsalis had straddled the decades with his trumpet playing and his excellence. I love Bob James (mentioned in another answer), but he is one of my favorite keyboard players. Though he has featured many other instruments in his recordings, they are are mostly keyboard music! Your question is not specific enough, especially when it comes to jazz. You will get answers from all over the place and many of them won't even include sax or trumpet! Better you had asked for some song lists featuring sax or trumpet. Chris Bodie (sp.?) is a very popular trumpet player these days, because he recorded with Sinatra and is still going strong. I hear him on many radio stations. Michael Brecker was one of the most popular sax players, but he died a couple years ago. However, you hear him on many hit song recordings, such as Billy Joel's JUST THE WAY YOU ARE. His brother, Randy is a fantastic trumpet player and the two of them were in many bands together such as The Brecker Brothers and Dreams (with Billy Cobbham on drums). They recorded many of the classic CTI jazz classics with drummer Steve Gadd and others. In an earlier era, the Adderley Brothers made sibling jazz with Cannonball on sax and Nat on trumpet. You just give us no clues as to what that melody you are searching for really sounds like. Is it funk? Straight-ahead? Bebop? Fusion? There are too many possibilities!