In a saucepan, add 1 cup blueberries, lime juice, and 2-3 tablespoons water. Turn the heat on to medium, and cook the berries for about 2 minutes. After 5 minutes, reduce the heat to low, and cook the berries, stirring occasionally until half the berries have burst and the liquid has thickened.
Add the sugar and stir it in. Cook for 5 minutes and then add the remaining cup of blueberries. Increase the heat to medium and simmer, stirring occasionally. Continue cooking until the compote thickens and most of the berries have softened.
Use immediately or store in the refrigerator for up to 1 week. Serve hot with pancakes, waffles, French toast, or scones. You can use this with oatmeal, yoghurt, ice cream, pudding, custard, and with cheesecake.