Combine dried elderberries, cold water, lime zest and ginger in a pot and bring to a boil. Reduce heat and simmer until the liquid has reduced in half to approximately 1 cup.
Use a sterilized mason jar to preserve the syrup. Pour the water into the mason jar through a fine-mesh strainer. Use a clean cheesecloth to press the remaining elderberries into the stainer so more liquid flows into the jar.
Add the honey to the reduced liquid in the mason jar and stir until well mixed. Alternatively, put the lid on the jar and shake it well.
Make sure to label and store it in a cool, dry location like a pantry or your refrigerator. Once you open the jar, make sure to store it in the refrigerator for up to 3 months.