Peel and cut clementine segments in half. Peel and cut kiwi horizontally into 10 slices. Cut each slice in half. Set aside.
Add yogurt, honey, and vanilla to a bowl and stir to fully combine. Add clementines to yogurt mixture and combine.
Fill popsicle molds ¾ full with yogurt mixture. Add two kiwi half slices to the sides of each mold with the curved sides pointing down. The flat edges should be even with the top of the molds. Fill the remaining space with the yogurt mixture.
Add the popsicle lid and insert sticks so that about 1½ inches sticks out from the mold.
Freeze 4-5 hours or overnight before serving. For easy removal, fill sink with about 5 inches of hot water. Place the mold in the water for 20-30 seconds, then gently pull popsicles from the mold. Place the popsicles on a parchment lined baking sheet and cover with plastic wrap. Keep frozen until ready to serve.