In a shallow dish stir together the orange juice, lime juice, garlic, cumin, oregano, salt, and pepper. Add the portabella caps and spoon some of the orange juice mixture over top. Allow to marinate at room temperature for at least 30 minutes, and up to 3 hours, gently stirring and spooning some sauce over the mushrooms every so often.
To cook your portabella steaks on the grill, lightly oil the grate and set your grill to medium-high heat. Place the mushrooms directly on the grill and brush with a bit of the marinade. Cook for about 4 minutes, flip and cook for about 4 minutes more, until lightly charred and tender.
To cook your portabella steaks on the stove, coat the bottom of a large skillet with about 2 tablespoons of olive oil and place it over medium-high heat. When the oil is hot, add the marinated portabella caps and spoon a bit of the marinade over each. Cook for about 5 minutes, gently flip, and cook for about 5 minutes more, until tender.
Divide the portabella steaks onto plates and sprinkle with cilantro. Serve with excess marinade on the side for dressing.