Seed the limes, scoop out the section. Squeeze lime shells and reserve any juice. Combine lime sections, juice and water and cook for 20 minutes on low heat.
Increase heat to medium, add berries and sugar and continue cooking 20-30 minutes, or until thickened. Pour into 1/2 pint jars leaving 1/4" headspace, seal, process in Bwb 5 minutes. Makes about 7 half pints.