Combine the water, sugar and chopped rosemary in a pot, and bring to a low boil. Let simmer until the sugar dissolves, then turn off the heat, and leave the rosemary until it perfumes the syrup to your liking (overnight is preferable). Strain and keep in the fridge.
Place a few ice cubes in each martini glass.
Put some ice in a shaker, and add all the ingredients. Shake for 20 seconds and pour into the glasses.
Garnish with a rosemary sprig, decorated with a few fresh cranberries, and drop a few cranberries in the glasses for a more cheerful look.