The Grammy Award for Best Performance by an Orchestra or Instrumentalist with Orchestra - Primarily Not Jazz or for Dancing was awarded from 1959 to 1964. The award had several minor name changes:

• From 1959 to 1960 the award was known as Best Performance by an Orchestra
• In 1961 it was awarded as Best Performance by a Orchestra - for Other Than Dancing
• From 1962 to 1964 it has been awarded as Best Performance by an Orchestra or Instrumentalist with Orchestra - Primarily Not Jazz or for Dancing

This award was presented alongside the award for Best Performance by an Orchestra - for Dancing.

Years reflect the year in which the Grammy Awards were presented, for works released in the previous year.

1960s

• Grammy Awards of 1964
  • Al Hirt for "Java"
• Grammy Awards of 1963
  • Peter Nero for The Colorful Peter Nero
• Grammy Awards of 1962
  • Henry Mancini for Breakfast at Tiffany's
• Grammy Awards of 1961
  • Henry Mancini for Mr. Lucky
• Grammy Awards of 1960
  • Dave Rose & Dave Rose for Like Young performed by Dave Rose & His Orchestra with Andre Previn

1950s

• Grammy Awards of 1959
  • Billy May for Billy May's Big Fat Brass