Puree the grapes in a food processor or blender (you'll have about 2 cups.) Transfer to a medium-size pot and bring to a boil. Boil the grapes, stirring occasionally, until the mixture has thickened and reduced to about 1 1/2 cups, about 10 minutes. Transfer to a bowl, stir in the sugar and honey and let cool to room temperature.
Fold in the yogurt just until nicely swirled, then spoon into popsicle molds. Cover with foil, insert popsicle sticks and freeze for 4 to 6 hours or until set.