In a saucepan combine chopped rhubarb, sugar and water, bring to a boil and simmer over low heat for 7-10 minutes until rhubarb is very tender and falling apart. Cool.
Put the rhubarb syrup though a fine sieve and store in a clean, mason jar in a refrigerator for up to a month.
To make the martinis:
Put all the ingredients together into a cocktail shaker and shake vigorously for 30 seconds.
Pour the Rhubarb Martini through a cocktail strainer into the glasses. Always taste before pouring and add more syrup if too sour or more lime juice if too sweet.