With a sharp knife, cut peel colored part only from one of the grapefruit.
Then cut peel into long, thin slivers, place in a 1 1/2- to 2-quart pan, and add 1 cup water.
Bring to a boil over high heat; drain.
Repeat with 1 more cup water.
Set drained peel aside in pan.
Cut peel and all white membrane from outsides of remaining 4 grapefruit.
Holding fruit over a bowl, cut between membrane to release segments into bowl.
Squeeze juice from membrane into bowl; discard membrane.
Drain off juice and reserve.
Add cherries, 1/4 cup of the liqueur, and 1 tablespoon of the sugar to grapefruit segments.
Add reserved grapefruit juice, remaining 1 tablespoon sugar, and honey to drained grapefruit peel in pan.
Bring to a boil over high heat; boil, stirring often, until syrup is reduced to about 2 tablespoons about 5 minutes.
Stir in remaining liqueur.