Place sugar on a small plate, dip the rims of 2 martini glasses in water and then in the sugar. Put the glasses in the freezer to set.
Using a muddler, or the end of a rolling pin, muddle the strawberries and mint in a cocktail shaker (leave some fresh strawberries to garnish if desired).
Add the ice, Vermouth and Gin to the cocktail shaker and mix well.
Strain into the 2 martini glasses.
Add the fresh orange slices and strawberries to garnish.