Combine the pomegranate juice, grenadine, and sweetened lime juice in a container. Keep refrigerated until serving time.
To make an 8 oz glass, add roughly 2 tablespoons of the juice blend to the glass, then top off with lemon-lime soda. Adjust the amount of juice blend to taste.
For a punch bowl, place the juice blend in the bowl with ice cubes, lime wedges, and pomegranate arils. Gently add the lemon-lime soda.
Finish each serving with a couple of small lime wedges and a spoonful of pomegranate arils.