Prepare boiling water canner. Heat jars in simmering water until ready for use. Do not boil. Wash lids in warm soapy water and set aside with bands
In a large, deep, stainless steel saucepan, combine garlic, wine, wine vinegar, water, sugar, basil, oregano and balsamic vinegar. Bring to a full rolling boil over high heat, stirring occasionally. Reduce heat, cover and simmer 5 minutes or until garlic is heated through. Remove from heat.
Pack tomatoes into a hot jar leaving a ½ inch headspace. Ladle hot vinegar mixture over tomatoes, leaving a ½ inch headspace. Remove air bubbles. Wipe jar rim. Center lid on jar and apply band, adjust to fingertip tight. Place jar in boiling-water canner, making sure water covers jar by at least 1 inch. Repeat until all jars are filled.
Water must cover jars by 1 inch. Adjust heat to medium-high, cover canner, and bring water to a rolling boil. Process half-pint jars 20 minutes, adjusting for altitude. Turn off heat and remove cover. Let jars cool 5 minutes. Remove jars from canner; do not retighten bands if loose. Cool 12-24 hours. Check lids for seal, they should not flex when center is pressed