Combine 1 cup water with the agar-agar powder in a small saucepan over medium heat, whisking constantly for about 2 minutes until it fully dissolves. You want to make sure there are zero lumps floating around because they'll wreck the texture of your mango coconut popsicles. Once it's completely smooth, remove it from heat and let it cool for 3-4 minutes.
Pour your 2 cups mango puree into a blender along with the coconut milk, coconut water, and that cooled agar-agar mixture. Add the lime juice, lemon zest, cardamom, and sea salt. Blend on high for 45 seconds until everything's completely combined and you've got a gorgeous peachy-orange mixture.
Stir in the honey and granulated sugar by hand using a whisk — this takes about 30 seconds and helps the sweetness distribute evenly. Taste it right now and adjust if you need more sweetness (I usually don't, but everyone's palate is different).
Strain the mixture through a fine-mesh sieve into a large measuring cup, pushing gently on any pulp with the back of a spoon. This step takes maybe 2 minutes but removes any tiny bits that could create an icy texture. Don't skip this part because it's honestly the difference between smooth and gritty.
Pour the strained mixture into your popsicle molds, filling each one about three-quarters full — leave a little room for expansion as they freeze. Insert the sticks gently, making sure they're standing straight up. Room temperature pouring works best because cold mixture sets too fast and creates air pockets.
Place the molds on a flat, level shelf in your freezer for the first 2 hours (this keeps the sticks perfectly centered). After 2 hours, your tropical summer pops should be slushy enough to hold the sticks on their own at that point.
Let them freeze completely for at least 4 more hours, though I usually leave mine overnight for maximum creaminess. To remove them easily, run warm water over the outside of each mold for 15-20 seconds, then gently wiggle and push from the bottom. Store them in a freezer bag once they're fully solid so they don't get freezer burn.