Cut 4 large rectangles of aluminum foil. Place salmon fillet on each piece and evenly distribute tomatoes and kalamata olives. Drizzle evenly with olive oil, make sure there is olive oil underneath the salmon to avoid the skin sticking to the foil. Sprinkle evenly with salt and fresh pepper. Fold foil and crimp the edges to seal the packages.

Preheat grill to medium high heat, allow to reach 500F, add salmon packages and grill, covered for 4 minutes, and uncovered for another 4-6 minutes. Carefully remove to a baking sheet. Allow to rest until foil is cool enough to handle.

Open foil packages, drizzle with balsamic vinegar and sprinkle with basil. Serve immediately.