In a large nonreactive saucepan crush blueberries with a potato masher or back of a heavy spoon. Add vinegar, sugar, lime and cinnamon; bring to a boil. Reduce heat and simmer covered, for 20 minutes. Cool slightly and pour into a large bowl. Cover and refrigerate for 2 days to allow flavors to blend.

Place a wire mesh strainer over a large bowl. In batches, ladle blueberry mixture into strainer, pressing out as much liquid as possible. Discard solids.

Pour vinegar into clean glass bottles or jars; refrigerate, tightly covered, indefinitely. Use this in salad dressings (as below) or drizzled over grilled chicken or beef.