1. In a bowl, mix apricot nectar, orange juice, honey, mustard, and horseradish. Rinse meat and put in a plastic food bag; add 1/3 cup of the apricot sauce. Seal bag and let stand 15 to 20 minutes, turning occasionally. Reserve remaining apricot sauce.
2. Cut apricots in half and discard pits. Lift steaks from bag and discard the marinade.
3. Lay steaks on a grill over a solid bed of hot coals or high heat on a gas barbecue (you can hold your hand at grill level only 2 to 3 seconds). Lay apricot halves on grill and brush with some of reserved apricot sauce. Cook steak, turning once, until done to your liking, 8 to 10 minutes total for medium-rare (pink in center, cut to test). Cook apricots until hot and lightly browned, about 5 minutes total; as cooked, transfer to a platter and keep warm.
4. Heat the rest of the reserved apricot sauce until boiling in a microwave-safe bowl in a microwave oven at full power (100%) or in a pan on direct heat. Serve sauce with steaks and apricots, adding salt and pepper to taste.