Cut off mushroom stems even with caps; discard stems. If you like, remove gills. Lightly rinse mushroom caps. Gently pat them dry with paper towels.
In a small bowl, combine the soy sauce, olive oil, vinegar, garlic, salt and black pepper. Lightly brush the tops of the mushrooms with some of the soy sauce mixture.
Grill mushroom caps, top side down, on the rack of a covered charcoal or gas grill directly over medium heat for 5 minutes, brushing grill sides with remaining soy sauce mixture. Turn and grill 5 to 7 minutes more or until slightly softened and tender.
To serve, the grilled portobello mushrooms can be eaten like steaks, sliced and tossed with pasta, or served in a salad, rolled in tortillas with grilled red sweet peppers, or slipped between slices of grilled focaccia or in sandwich buns.