Soak wooden skewers in water for at least 30 minutes prior to cooking.
Brush shrimp with the olive oil. Combine seasonings and coat the shrimp on all sides. Slide the shrimp on the skewers. Slide the tomatoes on a separate skewer
Grill shrimp for approximately 7 minutes on each side, just until the shrimp is pink and opaque. Add the tomatoes to the grill to cook during the last 7 minutes.
In the meantime, cook the linguine according to package directions in salted water. Just before draining the pasta, reserve 1 cup of the cooking water and set aside.
After draining the pasta, return the pot to the stove and melt the butter. Return the pasta to the pot and add the parmesan cheese. Stir until the cheese is melted and the sauce is slightly creamy, adding reserved water as necessary to keep pasta moist.
Pile the warm linguine onto four plates. Add the grilled shrimp and cherry tomatoes. Sprinkle with chopped basil and additional Parmesan cheese, if desired.