Bring the water, lime juice and raspberries to the boil and simmer for approx. 2 mins. Turn off the heat, cover and leave on the hob to steep for approx. 15 mins. Press the berries and the liquid through a sieve.
Bring the juice, sugar, cinnamon, vanilla and cardamom to the boil, stirring constantly. Reduce the heat and simmer for approx. 2 mins. While still boiling hot, ladle the syrup into the clean, warmed bottle and fill to just below the brim, seal immediately, leave to cool.
To serve, dilute approx. 2 tbsp of syrup in approx. 200 ml of water.