Trim and discard any fat on lamb racks down to about 1/8 inch thick; rinse lamb.
In a deep bowl, mix wine, 1/2 cup port, vinegar, shallots, thyme, and pepper. Add lamb and turn to coat well. Cover bowl airtight and chill for 1 to 4 hours, turning racks occasionally.
Lift racks from marinade, draining well; reserve liquid.
Place a 10- to 12-inch nonstick frying pan over medium-high heat. When hot, lay lamb racks, one or two at a time (don't crowd), meat side down, in pan. Brown entire meat side, tipping racks back and forth as necessary, 4 to 5 minutes total per rack. Frequently drain and discard any fat in pan to reduce spattering. As browned, return racks to marinade and coat well. Cover airtight and chill another 1 to 4 hours, turning racks occasionally.
Lift racks from bowl and lay, bones down (bones can overlap), in a shallow 12- by 17-inch pan. Pour marinade over lamb.
Bake in a 450° regular or convection oven until a thermometer inserted into meat in the center of a rack, parallel to rib bones, registers 125° for rare, 15 to 18 minutes, or 135° for medium-rare, 25 to 27 minutes (meat should still give easily when pressed). If marinade evaporates, add about 1/4 cup water to pan and tilt to mix, to prevent scorching. Transfer racks to a platter and let stand at least 5 minutes.
If desired, add 1/2 cup port and 1/4 cup water to pan; stir over high heat, scraping browned bits free, until mixture is boiling vigorously. Drain any accumulated juices from lamb into pan, then pour pan juices into a small bowl.
Cut racks apart into double lamb chops. Serve with pan juices. Add salt to taste.
* Percent Daily Values are based on a 2,000 calorie diet. Your daily value may be higher or lower depending on your calorie needs.