In a medium sauce pan combine 1 cup of the blueberries, the water, sugar and lime or lemon juice. Cook and stir over medium heat for 2 to 3 minutes or until sugar dissolves. Bring to boiling. Reduce heat and simmer, uncovered, for 15 to 20 minutes or until slightly thickened, stirring occasionally.
Stir in remaining 1 cup blueberries and cook, stirring occasionally, 2 to 3 minutes more or until blueberries become soft. Serve warm. Cover and refrigerate remaining syrup for up to 1 week.