Halve and remove the seeds from the pomegranates, saving any juice in a bowl. Add with pomegranate juice, 250 ml (approximately 8 ounces) of water, the grape juice, rum, and sugar to a pot. Halve the lime, and squeeze the juice into the pot. Bring to a boil, stirring occasionally. Boil for 4 minutes.
Add the pomegaranate seeds, and the zest from the lime. Mix thoroughly and divide into the prepared jars. Seal, turn upside down, and let cool. Turn right side up and cool completely.