Preheat oven to 400°F. In a small bowl, whisk together orange zest, juice, soy sauce and ginger; set aside.
Cut 4 large pieces of parchment paper and place 1 salmon fillet onto each piece. Divide asparagus spears evenly among pieces of parchment, topping fillets. Pour orange-soy marinade over each fillet and, working with 1 piece of parchment at a time, wrap fillets in parchment paper. Bring top and bottom edges of parchment together. Pinch both parchment edges together at top and fold down in 1/2-inch sections, towards fillet. Fold each side of parchment in towards fillet in 1/2-inch sections.
Place parchment packets onto a baking sheet and bake for 15 minutes, or until salmon is solid and firm and asparagus is cooked through but al dente.