Chill your martini glass: Place your martini glass in the freezer for at least 15-20 minutes before you plan to make the cocktail. A well-chilled glass is key to a perfect martini.
Prepare the lychees: If using canned lychees, drain them from the syrup. Reserve 2-3 of the best-looking lychees for garnishing. You can optionally muddle one lychee in the bottom of your shaker for extra flavor, but this is not essential.
Combine ingredients: In a cocktail shaker, add the vodka, lychee liqueur, fresh lime juice, and simple syrup (if using).
Add ice and shake: Fill the cocktail shaker about two-thirds full with ice cubes. Secure the lid tightly and shake vigorously for about 15-20 seconds, until the outside of the shaker is frosty. This ensures the drink is well-chilled and properly diluted.
Strain and serve: Remove your chilled martini glass from the freezer. Double strain the mixture from the shaker into the glass using both the shaker's built-in strainer and a fine-mesh strainer to catch any ice shards or pulp.
Garnish: Spear one or two of the reserved lychees onto a cocktail pick and place it across the rim of the glass, or simply drop them into the drink.