Preheat the grill to high heat. Lightly coat the steak with oil and grill 5 to 7 minutes on each side for medium-rare. Season the steaks immediately with salt and pepper. Let the steak rest while you prepare the salad.
Lightly coat tomatoes with oil and grill 3 to 4 minutes.
To make the dressing, whisk together rum, apple cider vinegar, mustard and olive oil and then season with salt and pepper.
If you're using flank or skirt steak, slice the steak across the grain. Serve steak and grilled tomatoes on top of lettuce and toss with rum vinaigrette.