Place a few spoons in the freezer.
Combine the raspberries, lemon juice, rosemary sprigs and sugar in a medium pot over medium heat and bring to a boil, stirring frequently to help break up the berries.
Once the mixture hits a boil, reduce the heat to medium low and let it simmer for 15-20 minutes, again stirring frequently.
The mixture should thicken as it cooks. Once it's feeling nice and thick, pull out one of your freezer spoons. Pour a small drop onto the spoon and run your finger through it. If your finger leaves a track in the jam, it's done. If the jam runs into the trail your finger made, keep cooking a bit longer and then try again.
Pull out the rosemary sprigs, along with any leaves that fell off (there shouldn't be many). Remove from heat and pour into a clean jar or glass container to cool before adding the lid and storing in the fridge.