Place fruit and honey in a medium-size saucepan. Bring to a simmer, stirring frequently. The fruit should begin to break down while it cooks, but using a fork or potato masher will help with this as well.
In a small bowl, stir together cornstarch and water until cornstarch is dissolved; pour into fruit mixture. Simmer 5 minutes or until thickened and no longer cloudy, stirring often. Allow to cool.
Add two tablespoons fruit compote to each of 4 bowls or cups, then top each with 1/2 cup yogurt.