The Sam Browne belt was used from 1927-1940, and was dropped as a part of the uniform then. Thereafter, officers wore a plainer leather belt (or wool) with the dress blouse, and dress swords were mounted to the belt with a flat chain and frog assembly.
I am only familiar with the US Model of 1902 sword. The only method to attach this sword to the U.S. Sam Browne belt, is the method I described.