In a small saucepot over medium-high heat, combine water, blackberries, ginger and lemon juice. Bring to a boil, reduce to a simmer and cook until berries break down, about 5 minutes. Remove from heat and strain into a bowl, using the back of a spoon to push blackberry pulp through. Return blackberry mixture to the sauce pot, add sugar and bring to a boil. Lower the heat and simmer until reduced by half, about 20 minutes, stirring occasionally to avoid burning. Remove from heat and let cool.
Brush a baking sheet with olive oil and set fillets on top. Brush fillets with oil and season with salt and pepper. Once blackberry mixture is cool, brush over salmon fillets and bake for 4 minutes. Brush again with blackberry mixture. Turn oven to broil and broil another 3 minutes.