To make the raspberry syrup, place the raspberries in a heatproof bowl. Bring the water to the boil, then mix with the sugar in a separate heatproof bowl, stirring to dissolve. Pour this over the raspberries, cover with cling film and set aside for 2 hours. Strain when ready to serve.
Place 30ml raspberry syrup in a NutriBullet or blender along with the rum, lime juice and a scoop of ice and blitz. Serve in a martini or daiquiri glass and garnish with a lime slice.