Place the berries, sugar and water in a small pan, bring to the boil while stirring. Reduce the heat, simmer for approx. 5 mins., leave to cool, chill for at least 30 mins.
Puree the berry syrup, lime zest, lime juice and rum until smooth, pour into the glasses. Add the ice and reserved berries to the glasses, top up with the prosecco, garnish with herbs.