Combine the elderberries, water, cinnamon, cloves, and ginger in a small saucepan over high heat and bring the mixture to a boil. Lower the heat and allow the mixture to simmer until the water has been reduced by half, about 25 to 30 minutes.
Pour the cooked berries and liquid through a fine mesh strainer, into a clean bowl, to strain out the berry skins. Use the back of a spoon to press on the berries in the strainer, to extract all of the juice, then discard or compost the pulp that's left in the strainer.
Allow the elderberry juice to cool to room temperature. Stir in the honey, using a whisk to incorporate it smoothly, then transfer the syrup into a sealed glass jar that you can store in the fridge.