Jamaican Rum Punch is served for guests and it's THE party drink perfect for the holidays. With just a few ingredients this Rum Punch comes together beautifully. Drinking this drink just takes you to the beaches of Jamaica relaxing. Jamaican rum punch is a fruity drink with a rum base. This easy-to-make rum punch is made with simple ingredients; fruit punch, club soda, orange-pineapple juice, ginger, lime, syrup, pimento berries, and of course rum!