If using bamboo skewers, soak them in water for at least 30 minutes before grilling.
Make the kebabs: In a small bowl, mix the olive oil, lemon juice and tarragon. Set aside.
Alternate the salmon cubes, red bell pepper, zucchini and mushrooms on the skewers and place the filled skewers on a rimmed baking sheet or in a shallow baking dish.
Stir the olive oil marinade and brush it on the kebabs. Just before grilling, sprinkle kebabs with salt and pepper to taste.
Prepare the grill. If using a gas grill, set at medium for indirect cooking. If using a charcoal grill, start the charcoal or wood briquettes. When the briquettes are hot, distribute the heated charcoal evenly under the cooking area.
Oil the grate and grill kebabs over medium heat for 6 to 8 minutes, turning every 2 minutes and brushing kebabs with leftover marinade from baking sheet, if desired. Do not overcook or the salmon will dry out.
Remove kebabs from grill and let them stand, loosely covered, for 5 minutes before serving.