Preheat oven to 275F. Line a rimmed baking sheet with parchment paper. Pat salmon or arctic char dry with a paper towel, then place on the baking sheet.
In a small bowl, combine butter, chopped shallot, chives, dill, lemon zest, Kosher salt, and black pepper. Mix well, then spread evenly on top of the fish.
Bake until barely cooked through, (time may vary depending on the thickness of the fish — pull salmon out when it registers 120F in the center). Top with capers, then serve immediately with lemon wedges.