Preheat your oven to 400°F (200°C). Cut four pieces of aluminum foil, each about 18 by 12 inches (45 by 30 cm).
Brush the salmon fillets with 1 tablespoon (15 ml) of olive oil. Season the fish evenly with 1 teaspoon (6 g) of salt and 1/2 teaspoon (1 g) of black pepper.
Stir the remaining 2 tablespoons (30 ml) of olive oil, lemon juice, drained tomatoes, chopped shallots, capers, Italian seasoning, and the remaining salt and pepper together in a medium bowl.
Place one salmon fillet in the center of each piece of foil. Arrange a quarter of the cut asparagus next to each piece of fish.
Spoon the tomato and shallot mixture evenly over the top of each salmon fillet.
Fold the long sides of the foil together and crease them tightly to seal. Fold the short ends up to create a closed packet, leaving a little room inside for steam to expand.
Place the four sealed packets on a large rimmed baking sheet.
Bake for 16 to 22 minutes. The salmon is done when it flakes easily with a fork and reaches a safe internal temperature of 145°F (63°C).
Remove from the oven and carefully open the packets to release the hot steam before serving.