Place the sugar, zest and lemon juice in a pan over very low heat and stir until the sugar dissolves. Add strawberries and blueberries and cook for 20-30 minutes over low heat stirring occasionally.
To test for doneness, place a little jam on a cold plate (you can put the plate in the fridge beforehand), run your finger through the jam on the plate, and if it does not try to run back together, it is done.
Remove from the heat and transfer to jars. It keeps in the fridge for up to 2 weeks, or longer if the jars are sterilized.