In a 5-quart pot over medium-low heat, bring the red wine, port, cinnamon sticks, whole cloves, orange zest, sugar, rum, and brandy to a gentle simmer.
Stir until the sugar is dissolved and the mixture is steaming, but do not let it boil.
Taste and add more sugar if desired.
Cover the pot and keep the glogg warm over very low heat.
In a separate bowl, mix together the raisins and slivered almonds.
Ladle the glogg into coffee cups or small glass mugs.
Garnish each serving with a spoonful of the raisin and almond mixture.