In a 350 degree oven, roast strawberries with agave until tender. Cool completely.
Meanwhile, prepare the matcha mix by adding coconut milk to a blender with agave and blue matcha powder. Blend until completely smooth and all of the matcha has been well incorporated.
Even distribute the cooled strawberries among the popsicle molds. Be sure to push them down into the bottom.
Pour the blue matcha mix over and freeze until sold. Allow to come up to temperature enough to remove. You can also set the pops into a pan of warm (not hot) water to loosen them slightly. Serve immediately.