Mama Bear's mug size soaps are very small, about 2" in diameter and 3/4" tall. In comparison, Stirling soaps are 3" in diameter and 1 1/4" tall. Hope that helps!
I think Mama Bears makes all their soaps in a 'mug soap' size, although I don't know the dimensions and if it would work for your particular mug
Haslinger is 60mm or about 2 3/8"
Very high quality, one of my favorites.