Preheat grill to high heat.
Cut the radicchio into quarters. Place radicchio onto a hot grill and cook for about 30 seconds on each side.
In a small bowl, add Dijon mustard and honey. Add vinegar and combine. Slowly whisk in the oil until combined. Add tarragon. Season with salt and pepper to taste.
Place two wedges of radicchio onto each plate. Top each with one ounce of blue cheese. Drizzle with vinaigrette and garnish with fresh tarragon.