How to make a perfect Candy Cane Martini. What you will need: Bacardi Rum, Peppermint Schnapps, Grenadine. What to do: Take your shaker and fill it up with ice. Add 2 oz. White rum. Add 1oz. Peppermint Schnapps. Add 1/4oz Grenadine to shaker. Shake to mix the ingredients. To get a candy cane look, mix white and red granulated sugar. Put Peppermint Schnapps on a saucer and dip the glass in it, then dip the glass in the sugar mixture. Now add the martini. Just follow these instructions and you will be enjoying a candy cane martini in no time.