The F-104H was a projected simplified version of the F-104G with less sophisticated and less costly equipment. It was designed for export to nations which wanted a Mach 2-capable fighter but which could not afford the full-blown all-weather F-104G version. An optical gunsight was to be fitted in place of the NASARR of the F-104G. A two-seat version was also proposed, which was to be designated TF-104H.
Very little interest was expressed by anyone for the F-104H or the TF-104H, and neither version ever got past the initial design stage.