In 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 boil gently, for 5 minutes, until garlic is heated through. Remove from heat.
Pack tomatoes into hot jars to within a generous 1/2 inch of top of jar. Ladle hot vinegar mixture into jar to cover tomatoes, leaving 1/2 inch headspace. Remove air bubbles and adjust headspace, if necessary, by adding hot liquid. Wipe rim. Center lid on jar. Screw band down until resistance is met, then increase to fingertip-tight.
Place jars in canner, ensuring they are completely covered with water. Bring to a boil and process for 20 minutes. Remove canner lid. Wait 5 minutes, then remove jars, cool and store.