While the fruit is roasting, blend together the Greek yogurt and lemon juice in a medium bowl. Mix in honey to taste, until it is barely sweet enough for your liking (keep in mind that the berries will be very sweet). Add more lemon juice if you want tart popsicles.
Preheat oven to 350 degrees Fahrenheit. Line a rimmed baking sheet with parchment paper. In a medium bowl, gently toss berries with the sugar, a dash of sea salt and 2 tablespoons honey. Pour the berries onto the prepared baking sheet and arrange the berries in a single layer. Roast for 30 minutes, stirring halfway, or long enough for the berry juices to thicken but not burn (watch the edges in particular).