In a large stainless steel, enamel, or nonstick heavy saucepan, combine tomatoes, onion, sweet pepper, dried cherries, vinegar, sugars, the water, lime juice, ginger, salt and garlic.
Bring to boiling, stirring occasionally, reduce heat. Simmer covered for 25 minutes stirring occasionally.
Stir rhubarb into tomato mixture. Simmer, covered, for 10 minutes. Uncover; simmer about 5 minutes more or until thickened.
Ladle hot chutney into hot half pint jars, leaving a 1/2 inch headspace.
Wipe jars, adjust lids and water bath for 10 minutes starting timing when the water come up to a boil. Make 3 half pints.