Combine the sugar, corn syrup, a pinch of salt, and 1/4 cup water in a heavy-duty 4-quart saucepan. Cook over medium heat, whisking frequently, until the sugar is dissolved, 4 to 5 minutes. Raise the heat to high and bring to a boil, brushing down the sides of the pan with a damp pastry brush to dissolve any sugar crystals. Boil, without whisking, until the mixture begins to color. Continue to cook, swirling the pan for even caramelization, until the caramel turns dark brown, about 7 minutes.
Immediately remove the saucepan from the heat. Quickly add the cherries and cream—be careful, the mixture will spatter. Set the saucepan over low heat and cook, whisking constantly, until the caramel is completely fluid with no lumps, about 2 minutes. Remove the pan from the heat and whisk to cool for a couple of minutes.
Scoop the ice cream into bowls, top with the sauce, and serve immediately.