Put the shrimp into a zip bag or nonmetallic container, add a little teriyaki sauce, and refrigerate for 2 hours or a little longer. Rig for grilling, preferably over charcoal or wood coals. Mix a basting sauce using half butter and half fresh teriyaki sauce (not the leftover marinade). Drain the shrimp, place them on a rack about 4 inches over the coals, and grill for 4 or 5 minutes on each side, basting several times. Serve hot.