Bring a large pot of salted water to a boil.
Preheat a grill or grill pan to medium heat. In a medium bowl, toss tilapia strips, tomatoes and artichokes with 3 tbsp. of the parsley and 2 tbsp. EVOO. Season with salt and pepper.
Thread tilapia strips, grape tomatoes and artichoke hearts on 8 skewers. Grill skewers, turning once, until fish is opaque, 9 to 11 minutes.
Meanwhile, add the orzo to the boiling water and cook until al dente, 8 to 10 minutes. Drain, transfer to a bowl and toss with the remaining 1 tbsp. parsley and EVOO. Season with salt and pepper.
Serve skewers with orzo and lemon wedges.