In a small pot, simmer ½ cup water, sugar, and raspberries over medium heat until the sugar is dissolved. Use a wooden spoon to gently muddle the raspberries in the pot.
Strain the mixture through a fine-mesh strainer into a bowl. Use the back of a spoon to press on the raspberries to extract all the juice.
Juice the limes and combine the lime juice into the raspberry mixture. It will make about 1 ⅓ cups of syrup.
Divide the raspberry syrup between 4 glasses and top with sparkling water or still water.