Combine the berries, sugar, lemon zest and juice in a medium saucepan set over medium heat. Bring to a boil and cook until the berries burst and the liquid starts to thicken, about 5 minutes.
Strain the mixture through a fine-mesh sieve, forcing the berries through by pushing and scraping with a rubber spatula. The more you force through, the thicker the sauce will be (the pulp closest to the seeds contains the most pectin, which is a natural thickener). Let cool completely and store in the refrigerator until ready to serve.
This sauce is delicious on top of ice cream or your favorite dessert. Top with crumbled cookies, crumbled pound cake, caramel popcorn, chocolate-covered pretzels or brownie pieces.