Trim the tenderloins of all fat and silverskin. Place them in a shallow baking dish large enough to hold them without crowding.
Combine the soy sauce, sherry, honey, vinegar, oil, and orange juice in a medium bowl, whisking until well blended. Stir in the rosemary, shallots, and ginger. Pour the mixture over the tenderloins. Cover with plastic wrap and allow to marinate at room temperature for 2 hours.
Preheat an outdoor grill or indoor grill pan.
Remove the pork from the marinade, shaking off any excess. Place the tenderloins on the grill and cook, turning frequently, for about 18 minutes, or until an instant-read thermometer inserted into the thickest part reads 155 degrees F. Transfer to a platter and allow the meat to rest for 10 minutes before carving.
Meanwhile, place the marinade in a small saucepan over medium heat and bring to a simmer. Simmer for 10 minutes, or until slightly thickened.
Slice the pork into 1/4 inch-thick slices, spoon the hot marinade over the pork. Serve with a tossed salad.