Do not core the fennel before grilling. The core will hold the slices of fennel together.
Cut fennel bulbs vertically into 1/2-inch slices. Cook in boiling water to cover 3 minutes; drain. Combine fennel and radicchio in a large bowl; set aside.
Combine orange juice and next 6 ingredients in a jar. Cover tightly, and shake vigorously. Chill 1/4 cup vinaigrette; pour remaining vinaigrette over fennel and radicchio, tossing to coat. Let fennel mixture stand 15 minutes; drain.
Coat grill rack with cooking spray; place on grill over medium-hot coals (350 to 400 degrees). Place fennel on rack; cook, covered, 15 minutes, turning once. Add radicchio; cook, covered, 2 minutes. Toss fennel and radicchio with reserved vinaigrette.