Gently simmer the red wine, port wine, cinnamon sticks, whole cloves, and orange peel in a large pot set over medium-low heat. Stir in the sugar, rum, and brandy. Continue simmering 5 minutes more, stirring to completely dissolve the sugar, and the mixture is steaming but not boiling.

Mix the raisins and almonds together in a bowl.

To serve, ladle into coffee cups or Swedish-style small glass or ceramic mugs. Garnish each cup with a spoonful of the raisin and almond mixture.