Begin heating a skillet. Using a sharp knife, make several incisions in the skin of each breast in a criss-cross pattern (be careful not to cut into the flesh).
When the skillet is nice and hot, sear the duck breasts skin side down. Cook for about 15 minutes, spooning off the fat as it melts. Turn the duck breasts over and cook briefly, about 3 minutes. Remove from the skillet and allow them to rest under aluminum foil for 10 minutes.
Cut each breast widthwise into 6 slices.
The skillet should still be hot: pour in the honey and then the orange juice and zest, and return to low heat. Stir until the ingredients come together smoothly to form a sauce.
Place the duck slices on a serving platter and pour the sauce over them.
Serve the duck breast slices hot with the caramelized sauce, accompanied by the caramelized turnips.