If using wooden skewers, soak them in water in a casserole dish or baking sheet for 30 minutes prior to grilling. Prepare a grill or grill pan for medium-high heat; oil the grill grates with olive oil.
Mix the balsamic, lemon juice and mustard in a small bowl. Add the olive oil in a slow stream while whisking. Season with salt and pepper.
Thread the fish, fennel and tomatoes onto 8 skewers, alternating between fish and vegetables. There should be roughly 3 pieces of fish per skewer. Season all sides of each skewer with salt and pepper. Brush the balsamic mixture over all the skewers.
Add the skewers to the grill and cook until there are clear grill marks on the flame side, 3 to 5 minutes. Flip the skewers and cook for an additional 3 to 5 minutes. Continue to rotate the skewers and cook on each side until all sides are cooked and have a slight char.