Preheat oven to 400°F. Place 1 pound of cherries in a baking dish and drizzle them with the balsamic vinegar and honey, then sprinkle sea salt over the top. Roast for 35 minutes, stirring halfway through the cooking time, until cherries have released their juices and just begun to wrinkle a little.
Allow cherries to cool slightly, then transfer to a blender, making sure to scrape up all the pan juice too. Add the coconut milk and cornstarch and blend together. Taste and add additional honey or salt, if needed.
Cut remaining 1/4 pound of cherries in half; add to the Popsicle molds, and fill with cherry mixture. Use a skewer or chopstick to break up any air bubbles in the mixture, leaving a gap at the top of each mold for adding shredded coconut. Pop the molds into the freezer for 30 minutes.
Remove from the freezer and sprinkle the top of each mold with the shredded coconut, then snap on the lid and slide Popsicle sticks into each carefully. Return to the freezer and freeze until solid, for 6 hours or overnight.