Cut the honeydew melon in half. Scoop out the seeds and cut off the rind. Chop honeydew and add it to the blender. Taste some melon to see how much sugar you would need.
Squeeze lime juice into the blender and add mint.
Add 2-4 Tbsp of sugar and blend everything until all smooth. (*Optional: add rum if you making boozy popsicles.)
Divide honeydew mixture among popsicle mold cups. Freeze popsicles for at least 8 hours.
*If your mold doesn't have tops, use wooden popsicle sticks: cover the mold tightly with saran wrap and quickly poke wooden sticks through the center of each mold. Saran wrap will keep the sticks standing up while the popsicles freeze.
If you don't want to use saran wrap, you can set the timer for 1 hour and place ice pops molds in the freezer. After an hour, slide popsicle sticks into the center of each mold and then let it freeze for another 7 hours.*
*Remember, taking pops straight from the freezer can be quite hard. You will want to either run each mold under warm water (not over the top) or dip it in warm water for a few seconds so they can slide out easily.