Heat maple syrup in a saucepan, add lime zest and ginger. Let cool and store in the refrigerator.
Wash the duck breasts, remove the tendons and excess fat, then use a sharp knife (possibly a carpet knife) to cut into the skin very finely, diamond-shaped. Heat the maple syrup in an ovenproof pan. Let the duck breasts caramelize really nice and hot on the skin side. Lift the meat every now and then so that the duck breasts are actually in the syrup. When the skin is caramelized, just fry briefly on the meat side.
Remove the duck breasts from the pan. Place a wire rack or wire rack on the pan, place the duck breasts on top and place in the preheated oven at 200 degrees for 8 minutes.
For the port wine and balsamic vinegar sauce, reduce in a small saucepan until only 3-4 tablespoons remain.