Combine the elderberries, water, and ginger (if using) 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 20 minutes.
Transfer the cooked berries and liquid to a clean bowl and pour it through a fine mesh strainer to remove 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 the small amount of pulp left in the strainer.
Allow the elderberry juice to cool to room temperature, so that the heat doesn't harm the nutrients in the honey, then stir in the honey. Use a whisk to incorporate it smoothly, then transfer the syrup into a sealed glass jar that you can store in the fridge.
This syrup should keep well for at least two weeks when stored in the fridge, so if you don't think you'll use it all before then, feel free to freeze any extras. You can always thaw it overnight in the fridge when you need more. Homemade elderberry syrup doesn't become as thick as the store bought version because it uses less sugar and no preservatives or thickeners, so don't be alarmed if the final syrup has a more liquid consistency.