Preheat oven to 350 degrees F (175 degrees C). Butter a baking sheet so that the bottoms of the packets will brown when baked.
Prepare 4 sheets of parchment paper by folding each sheet in half and placing a tilapia fillet centered onto one side of the fold of each sheet. Season the tilapia with salt and black pepper. Top the fillets with equal amounts of tomato, garlic, basil, and capers. Sprinkle lemon juice over the fillets. Place 1 tablespoon butter atop the fish. Drizzle white wine over the fillets.
Roll up the sides of the paper first, then the top, leaving 1/2-inch space along one edge; fold to seal. Grease the bottoms of the packets with 1 tablespoon butter and arrange on the baking sheet.
Bake in preheated oven until the fish flakes easily with a fork, 15 to 20 minutes.