Drain tofu and remove from package.
Cut tofu into ¾-inch slices and lay out flat between paper towels.
Put weighted cooking sheet on top and press tofu, for 30 minutes. (This will remove water from tofu and allow marinade to soak up.)
While tofu is draining, mix together soy sauce, rice vinegar, sesame oil, honey, and ground ginger in medium bowl.
Marinate drained tofu in mixture for at least one hour.
Preheat Indoor/Outdoor Grill on setting 4 and grill tofu for 3 minutes per side.
Remove from grill and serve immediately with rice and vegetables.