Place all of ingredients except the honey or maple syrup into a blender. (When using frozen bananas, it’s helpful to break them into chunks.) Blend until very smooth, scraping down the sides of the blender as needed.
Taste the mixture and add the honey or maple syrup according to taste, blending to evenly distribute.
Pour the mixture into the popsicle molds.** If you are using wooden craft sticks instead of sticks that attach to the molds, set a timer for 1 hour and insert the sticks at this time. (If starting with frozen bananas, set the time for 30 minutes.) Optionally, place a piece of foil or plastic wrap over the molds and poke the stick through the foil or wrap. This will hold the sticks upright.
Place the popsicles in the freezer. They will be easier to remove from the molds when frozen overnight. To easily remove the molds, dip them in a glass of warm water, checking every 10 seconds or so, or until the molds pull away from the popsicles.