Place 2 cups of the cubed pineapple in a blender; add 3 cups of the water. Cover and blend until nearly smooth. Press mixture through a fine-mesh sieve into a large pitcher; discard solids. Repeat, using the remaining 2 cups cubed pineapple and the remaining 3 cups water.
Stir honey and lime juice into strained mixture. Pour into a serving pitcher. Cover and chill.
To serve, add ice cubes and if desired, pineapple wedges and/or lime slices to juice mixture.