In a small saucepan, over high heat, bring the cranberries, orange juice, water, your choice of sweetener, orange slices and cinnamon stick to a boil. Reduce the heat to medium and continue to simmer for 10 minutes.
Strain through a fine mesh sieve, using a spoon to push the syrup and juices from the cranberries through. Discard the berries, orange slice and cinnamon stick. Allow the syrup to cool, then add the lime juice and mix to combine.
To make a single cocktail, combine the tequila, triple sec and cranberry orange simple syrup in a glass rimmed with either coarse salt or sugar* over ice. Stir to combine. Add additional fresh lime juice to taste.
To make a pitcher of margaritas, combine the tequila, triple sec and cranberry orange simple syrup in a glass pitcher. Serve over ice in glasses rimmed with either coarse salt or sugar* and add additional lime juice to taste.
*To rim the glass with salt or sugar, just run a lime or orange around the rim of the glass, them immediately dip the rim into the salt or sugar in a flat dish.
Notes
The syrup will be thick and jammy. This is normal. It will blend in perfectly once mixed.