1. Simmer 5 ounces of pomegranate juice in small saucepan over medium-low heat until reduced by half, about 5 minutes. Transfer to bowl, add to remaining 9 ounces pomegranate juice, and stir in lime juice.
2. Place fine-mesh strainer over medium bowl. Prepare ice bath in large bowl.
3. Whisk together sugar, salt and egg yolks in medium saucepan. Whisk in cream and cook, stirring constantly, over medium-low heat until mixture registers 180 degrees.
4. Pour custard through strainer set over medium bowl. Whisk in pomegranate juice mixture, and set in ice bath. Allow to cool to room temperature, then cover and refrigerate at least 8 hours.
5. Transfer to ice cream maker. Freeze in ice cream maker according to manufacturer’s instructions. Once ice cream starts to thicken, add pomegranate seeds. Transfer to glass or plastic container, press plastic wrap or waxed paper against surface of ice cream, and cover with tight-fitting lid. Freeze until firm, at least 8 hours and preferably 24 hours. Ice cream will keep, frozen, up to 5 days.