Combine the first 3 ingredients in a medium saucepan over medium-high heat. Bring to a boil; reduce heat, and simmer 3 minutes. Place peach mixture in a blender; let stand for 20 minutes. Remove center piece of blender lid (to allow steam to escape); secure blender lid on blender. Place a clean towel over opening in blender lid. Blend until smooth. Pour into a large bowl. Refrigerate for at least 3 hours.

Press peach mixture through a sieve over a bowl, reserving liquid; discard solids. Stir in lime juice. Place 1/2 cup ice in each of 8 glasses. Pour about 2/3 cup limeade into each glass; garnish each glass with 1 peach wedge.