Cook the sausage according to the directions on the package and cut it into 1-inch rounds. Cut the basil leaves lengthwise into thirds.
Put an olive half about 1/3 of the way down onto a skewer. Then add 1 strip of basil, folding so it fits nicely on the skewer. Follow with 1 grape tomato and a round of sausage. Position everything on the end of the skewer so the skewer can stand up on its sausage end.