Combine marinade ingredients in a small bowl. Place the skirt steaks in a gallon-size, re-sealable plastic bag and pour the marinade in over the beef. Seal the bag and shake it all up to coat the meat entirely. Refrigerate for 20 minutes.
Preheat the broiler.
Place the blueberries and sugar in a small nonstick saucepan. Cook over medium-high heat for 1-2 minutes until sugar is melted and the sauce thickens. Set aside to cool slightly.