Step 1: Place the cherry soda, cherries, cherry preserves, lemon zest and juice, butter, sugar, cinnamon, and 3 tablespoons of wine in a heavy saucepan and gradually bring to a boil over medium heat. Reduce the heat and gently simmer the sauce to cook the cherries and concentrate the flavors, 5 minutes.
Step 2: Place the remaining 1 tablespoon wine and cornstarch in a small bowl and stir to form a slurry (thick paste). Whisk this paste into the sauce. Bring the sauce to a boil: it will thicken.
Step 3: Correct the seasoning, adding salt, pepper, sugar, or lemon juice to taste: the sauce should be highly seasoned.