In a small sauce pot, add the blueberries, thyme, sugar, balsamic vinegar, lemon juice, and ¼ teaspoon of salt. Place over medium heat. Boil for 15 minutes, stirring occasionally. The blueberries will release their juices. The sauce will reduce and thicken.
In the meantime, place an oven rack 6 inches from the broiler. Preheat oven broiler to high.
Pat salmon filets dry with paper towels. Sprinkle both sides of the fish with a pinch of salt and pepper.
Place the fish skin side down on the baking sheet.
Brush a thin layer of the blueberry glaze onto the salmon. Place the fish under the broiler for three minutes. Brush an additional thin layer of glaze on the fish. Place back under the broiler for an additional 3-5 minutes.
Once cooked, the salmon should flake when pressed with a fork, but not be dry.