In a small saucepan, combine the 3/4 cup of water and 3/4 cup of granulated sugar. Heat over medium heat, stirring until the sugar completely dissolves. Once dissolved, remove from heat and let it cool.
While the syrup is cooling, juice the limes. You’ll need about 1/4 cup of fresh lime juice, depending on the size of your limes. Set aside.
In a large mixing pitcher, combine the cooled simple syrup, the lime juice, and the unsweetened cranberry pomegranate juice. Stir well to combine.
On a small plate, pour the additional 1/4 cup of granulated sugar. Moisten the rims of your glasses with a lime wedge, then dip each glass into the sugar to coat the rim.
Fill the prepared glasses with crushed or cubed ice. Pour the juice mixture over the ice, filling each glass about 2/3 full.
Top off each glass with sparkling water or club soda, giving it a gentle stir to mix.
For an extra touch, garnish each glass with a few pomegranate arils and a lime wedge. Serve immediately and enjoy the effervescent delight of your sparkling pomegranate juice!