How to Make a Pink Martini. Pink martinis are the perfect drink for a pink-themed girl party or anytime you want to impress your guests with a special concoction. Also called a cosmopolitan, the pink martini is a combination of smooth white liquors and a tough of juice. These potent potions look elegant in a triangular cocktail glass. Guests will like watching you assemble, shake and serve up this popular drink. Be a thoughtful host or hostess and serve alcoholic drinks responsibly.