After pressing the tofu, place the cut up tofu into a bowl or container and add the marinade. Let sit for 20 minutes, turning on occasion so the marinade reaches all parts of the tofu.
Thread the skewers alternating vegetables and tofu. Place on a baking sheet or plate while you finish making the skewers and until you are ready to cook. Drizzle the remaining marinade over the skewers and add a bit of salt and pepper to taste.
Heat up an outside grill or indoor grill pan. When hot, add the skewers and cook on all sides until vegetables are cooked and tofu is heated through about 15-20 minutes.