Preheat the oven to 425 degrees F.
Zest half a lemon. Juice the lemon and 1 lime. Slice the remaining lemon and lime into very thin slices.
Place a few lemon and lime slices in the center of each parchment square. Place a fish fillet on top. (The citrus will help to keep the fish from burning on the bottom.)
In a bowl, whisk together the olive oil, 1 teaspoon salt, 1/2 teaspoon pepper and 1 teaspoon each lemon and lime juices, and drizzle over the fish. Top each piece of fish with a few slices of lemon and lime. Tightly fold the parchment paper into packages and make sure they are sealed well. Put the packages on a baking sheet and bake for 10 to 12 minutes, depending on the thickness of the fish.
Put the remaining citrus juices in a saucepan and bring to a boil over medium heat. Reduce by half, stirring frequently. Add the sherry vinegar, honey and 1 teaspoon salt.
Mix the parsley, garlic and lemon zest together with a slight pinch of salt and pepper for the garnish.
Place each parchment packet on a plate with a rim. Carefully tear or cut open the parchment packets and drizzle the fish with a teaspoon of the citrus reduction and garnish with the parsley and lemon zest mixture.