Preheat oven to 450 degrees with a rack set in the lower third of the oven and another rack set 8 inches from the broiler.
Place vinegar, amaretto, port, wine, and fennel in a medium saucepan and bring to a boil over high heat. Continue boiling rapidly until syrupy and reduced to 1/3 cup, about 20 minutes.
Meanwhile, heat a large ovenproof skillet over high heat. Season both sides of duck breasts with salt and pepper. Add oil to pan, swirling to coat; add duck, skin-side down. Transfer pan to lowest rack in oven. Cook until skin is dark golden brown and meat feels firm (for medium-rare), 10 to 12 minutes. Transfer duck, skin-side up, to a rimmed baking sheet. Let stand 5 minutes.
Preheat broiler to the lowest setting possible.
Using a heavy skillet, crush almonds; spread in a thin, even layer. Spoon 1/2 teaspoon honey on the skin side of each duck breast; press into almonds to adhere. Return to baking sheet, skin-side up and fill in any gaps with remaining almonds. The whole skin side should be evenly coated.
Transfer baking sheet to broiler and broil until almonds are toasted and sugar starts to melt, about 7 minutes, checking occasionally to make sure the almonds don't burn before the sugar begins to melt. Remove from broiler and let stand 5 minutes before slicing.
Meanwhile, reheat vinegar mixture over low heat until hot. Whisk in butter, a tablespoon at a time, until emulsified; season with salt and pepper. Divide sauce among serving plates and top each with a duck breast. Serve.