Chill your martini or coupe glass in the freezer for at least 5 minutes before serving, or fill it with ice water while you prepare the drink to achieve the perfect frosty presentation.
Juice the lime and orange fresh. For 1 medium lime, roll it firmly on the counter before cutting to release maximum juice (you need about 1 oz/30 ml). Squeeze half a small orange for the 0.5 oz/15 ml orange juice.
Fill your cocktail shaker halfway with ice cubes. Add the cranberry juice (3 oz/90 ml), fresh lime juice (1 oz/30 ml), fresh orange juice (0.5 oz/15 ml), and simple syrup (0.5 oz/15 ml).
Seal the shaker tightly and shake vigorously for 15-20 seconds until the outside of the shaker becomes frosty and cold to the touch. This chills and properly dilutes the mocktail for optimal flavor balance.
Remove ice from your chilled glass (if using ice water method). Using a fine mesh strainer, double-strain the mixture into the glass to catch any ice shards or pulp for a silky-smooth finish.
Gently top with sparkling water (1 oz/30 ml) by pouring slowly down the side of the glass to preserve carbonation.
Express the oils from an orange peel twist over the drink by holding it over the glass and giving it a firm twist, then run the peel around the rim and drop it into the drink. Thread fresh cranberries on a cocktail pick and rest across the rim, or tuck a mint sprig alongside the orange twist for an elegant aromatic finish.