Combine the water, sugar, and cranberries in a medium saucepan. Bring to a boil over medium heat. Lower to a simmer and cook for 5 minutes.
Strain the syrup through a mesh sieve, pushing on the cranberries to pop them and get the liquid out.
Cool the syrup before using it in cocktails. Store in an airtight container in the fridge for up to 1 week.
Martini
Fill a cocktail shaker with ice. Pour in the vodka, amaretto, and Grand Marnier. Secure the lid and shake vigorously until chilled.
Strain into a chilled martini glass. Slowly spoon in the cranberry simple syrup so that it sinks to the bottom of the glass.
Top off the martini with a splash of club soda and a squeeze of lime juice. Garnish with sugared cranberries and/or a lime wedge.
Notes
If you can't find fresh cranberries in the produce section, frozen fresh cranberries (in the freezer section) can be used. Thaw the bag overnight in the fridge and proceed to make the simple syrup as directed. Do not use canned cranberries or cranberry sauce.
The simple syrup recipes make about 1 cup of syrup, enough for 24 martinis.
To make sugared cranberries, dip cranberries in some of the simple syrup. Set the cranberries out on a plate to dry for 1 hour (while the rest of the syrup cools. The cranberries will be sticky. Roll them in sugar until coated.