Whisk together the lemon juice, orange juice, honey, olive oil, port, ginger, and garlic in a large glass or ceramic bowl.
Add the flank steak, and toss to evenly coat. Cover the bowl with plastic wrap, and marinate in the refrigerator 1 hour to overnight.
Preheat an outdoor grill for medium-high heat, and lightly oil the grate.
Cook the steaks until they are browned on the outside and red in the center, about 3 minutes per side. An instant-read thermometer inserted into the center should read 125 degrees F (52 degrees C). Slice the steak thinly across the grain before serving.
