In a heavy medium saucepan, add the sugar and ¼ cup water. Stir to blend.
Place over medium-high heat and bring to a boil without any stirring, washing down any crystals that form on the side of the pan with a pastry brush dipped in water.
Boil until sugar syrup turns the color of brewed tea.
Remove from heat and slowly add the remaining ¼ cup of water and whisk until smooth.
Slowly add rum and whisk to blend. Sauce will thicken as it cools.