Bring a large pot of water to a boil, add the sausages, and simmer for 8 minutes to remove some of the fat. Remove to a plate.
Melt the butter in a large 12x15 roasting pan on top of the stove.
Add the grapes and toss them to coat with butter.
Transfer the sausages to the roasting pan with tongs, nestling them down in the grapes in one layer.
Place in the oven and roast for 20-25 minutes, turning the sausages once, until they're browned and the grapes are tender.
Transfer the sausages and grapes to a serving platter with tongs and a slotted spoon and cover to keep them hot. Add the balsamic vinegar to the roasting pan and cook over medium-high heat for 2 minutes to reduce the balsamic vinegar slightly.