Gather your ingredients. Add blackberries, lemon zest, juice, and sugar into a small saucepan.
Heat ingredients over medium heat and bring to a simmer. Add a splash of vinegar.
Once the blackberries have broken down, taste - you may need to add more sugar or lemon juice.
Strain liquid and toss solids.
Mix warm water and cornstarch in a separate container.
While stirring constantly, add cornstarch mixture to blackberry juice.
Add combined mixture back to saucepan over low heat, stirring often, 5-10 minutes until it thickens.
Transfer to a jar. Serve warm or cooled. Refrigerate after it cools.