Combine rum, lemon juice and Tarragon Honeydew Syrup in a large container.
Place coconut milk in a separate container. Slowly pour rum mixture into coconut milk. Do not reverse this step. Pouring the acidic mixture into the milk slows acidification and creates finer curds for better clarification.
Refrigerate overnight.
The next day, strain mixture through a coffee filter set inside a fine-mesh strainer. Allow liquid to strain naturally without pressing.
If needed, strain liquid again through the same filter and curds for additional clarity.
Refrigerate until ready to serve.