For the simple syrup: Add the sugar and 1/3 cup water to a saucepan and set over medium heat. Bring to a simmer, stirring to dissolve the sugar, and simmer for 2 to 3 minutes. Let cool. (Can be made a day in advance and kept refrigerated.)
For the roasted grapes: Preheat the oven to 400 degrees F. Spray a baking sheet with cooking spray.
Put the grapes, stems and all, on the prepared baking sheet and sprinkle with the sugar. Roast until the grapes begin to burst a bit and lighten in color, about 20 minutes.
For the martini: To make each drink, add 8 to 10 grapes on the stem to a cocktail shaker and muddle with the bottom of a wooden spoon, making sure to crush all the grapes. Squeeze 1/2 of a lime into the shaker, add 2 tablespoons of the simple syrup and 3 ounces of vodka. Add a scoop of ice. Put the lid on the shaker and shake well. Strain into a martini glass and garnish with roasted grapes. Repeat with the remaining ingredients to make 4 martinis.