He married a fellow member of Celestin's Tuxedo Jazz Band, pianist Jeanette Kimball (née Salvant).
In the 1930s during the Great Depression Kimball switched to string bass to play in swing bands such as Sidney Desvigne's, but music did not provide enough money; he got a day job as a mailman.
He continued playing music in the evening, leading his band called "Narvin Kimball's Gentlemen of Jazz".
After World War II he formed a singing group called "The Four Tones" with Fred Minor, Alvin Alcorn, and Louis Barbarin that enjoyed some local success.
When Hurricane Katrina was threatening New Orleans, in 2005, Preservation Hall leader Ben Jaffe made a point to make sure Kimball and his wife were evacuated to Baton Rouge.