Coat a 3 1/2- or 4-quart slow cooker with cooking spray; set aside. Rinse salmon; pat dry with paper towels. Arrange salmon in the prepared cooker, tucking under any thin edges. Sprinkle salmon with garlic.
In a small bowl stir together mustard, honey, vinegar, and dill. Transfer 2 tablespoons of the mixture to another small bowl; stir in onion and broth. Drizzle broth mixture over salmon. Reserve the remaining mustard mixture until ready to serve.
Cover and cook on low-heat setting for 3 hours or on high-heat setting for 1 1/2 hours. If using low-heat setting, add Swiss chard for the last 30 minutes, stirring once halfway through cooking. If using high-heat setting, add chard for the last 15 minutes, stirring once halfway through cooking.
Carefully transfer salmon to a serving platter. Stir reserved mustard mixture into chard mixture; spoon onto platter with salmon. Drizzle with any remaining mixture in slow cooker. Makes 4 servings.