Process raspberries in a blender until smooth, stopping once to scrape down sides. Press mixture through a wire-mesh strainer into a small saucepan, using the back of a spoon to squeeze out juice. Discard pulp and seeds. Whisk in cornstarch until mixture is smooth; whisk in sugar.
Cook over medium heat, stirring constantly, until mixture boils. Boil 1 minute, stirring constantly; remove from heat, and cool.