Mash minced garlic and 3/4 t salt in a small bowl to form a paste, stir in oil.
Check the salmon for pin bones and remove if necessary. Measure out a piece of heavy-duty foil (or use a double layer of regular foil) large enough for the salmon fillet. Coat the foil with cooking spray.
Place the salmon skin-side down on the foil and spread the garlic mixture over it. Sprinkle with 1/3 C basil. Overlap tomato slices on top and sprinkle with the remaining salt and the pepper.
Transfer the salmon on the foil to the grill. Grill until the fish flakes easily, 10-12 minutes. Use two large spatulas to slide the salmon from the foil to a serving platter.
Serve the salmon sprinkled with the remaining 1/4 C basil.