Preheat the oven to 180C/350F/Gas 4.
Place one of the filo sheets onto a baking sheet and brush with some of the butter. Scatter over some of the almonds and coconut and drizzle over a little of the honey. Repeat until all the ingredients are used up. Brush the final layer of pastry with butter and a drizzle of honey.
Transfer to the oven to cook for about 5-7 minutes, or until golden-brown and crisp.
For the honey and orange syrup, heat the orange juice and honey in a pan and simmer until slightly reduced and syrupy. Add the orange segments, remove from the heat and stir to coat.
To serve, cut the baklava into triangles and serve on a plate with the honey and orange syrup spooned over the top. Drizzle the cherry juice around the edge of the plate.