I will start with one of the more popular beverages, spiced pomegranate drink. This drink is easy to make and very refreshing. This is very similar to Grenadine syrup, but please don't buy the commercial product when this drink is so easy to make.
Syrup of Pomegranates
Take a ratl of sour pomegranates and another of sweet pomegranates, and add their juice to two ratles of sugar, cook all this until it takes the consistency of syrup, and keep until needed. Its benefits: it is useful for fevers, and cuts the thirst, it benefits bilious fevers and lightens the body gently (Friedman, 2000).
Recipe
1 quart pomegranate juice
4 cups of sugar
1-2 cinnamon sticks*
Up to a tablespoon of cloves*
**One of the recipes I located while researching (Non Alcoholic Beverages of the Middle Ages by HL Ronan Meade) suggested the addition of cinnamon and or clove as well as other "warmed spices".
As the recipe from Al-Andulus suggests, equal parts of juice to sugar, heated until it boils and then lower the heat and cook until it becomes thick syrup. I dilute my syrup with a 4:1 ratio of water to syrup.
Works Cited
Friedman, D. (2000, September 4). Chapter One: On Drinks. Retrieved 14 2015, September, from An Anonymous Andalusian Cookbook of the 13th Century: http://www.daviddfriedman.com/Medieval/Cookbooks/Andalusian/andalusian10.htm#Heading506
Meade, R. H. (2002, October 25). Non-Alcoholic Beverages of the Middle Ages. Retrieved September 14, 2015, from Medieval Brewers Homepage: http://mbhp.forgottensea.org/noalcohol.html#_ftnref5