Pour the honey into a 2-cup glass measure. Microwave the honey, uncovered, at high, 30 seconds to make it pour easily.
Remove the measure from the microwave and add the oil, Worcestershire sauce, soy sauce, lime juice, garlic and onion powder. Whisk to blend well.
Place the meat in a gallon-size zipper-top plastic bag. Whisk the marinade once more and pour it over the meat. Seal the bag and turn the bag several times to cover the meat with marinade. Refrigerate 8 to 24 hours, turning the bag at least once, if possible.
Turn on a gas grill to medium high.
Remove the meat from the marinade and discard the marinade. Grill the meat, covering the grill to the desired doneness, 7 to 10 minutes per side for medium-rare, depending on the thickness. Do not overcook.
Remove from the grill and slice across the grain. Serve at once, or let stand until ready to serve. Refrigerate leftovers, covered, up to 3 days.