Prepare the mushrooms by trimming the cremini mushroom stems and/or removing the portobello mushroom stems. Clean the caps with a damp cloth or paper towel. Place the mushrooms on a large rimmed plate and drizzle generously with balsamic vinegar, olive oil, and tamari. Sprinkle with salt and pepper and use your hands to coat the mushrooms on all sides.

If using cremini mushrooms, thread them onto metal skewers (or wood skewers that have been soaked overnight).

Preheat an outdoor grill or grill pan to medium heat. Place the cremini skewers on the grill, or place the portobello mushrooms on the grill, gill side-up. Cook for 5 to 7 minutes per side, or until the mushrooms are tender.