Grenadine

Grenadine (from the French grenade — pomegranate) is a sweet syrup of pomegranate juice. Quite a few cocktails use grenadine, not only for flavor, but for the beautiful color it imparts. While there are some large commercial brands that are mostly high fructose corn syrup that is garishly colored, grenadine is simple to make at home, using one of three methods:

Cold Method
Shake equal parts by weight of pomegranate juice and sugar until as much sugar as possible dissolves into the liquid. It may take 10 minutes of shaking to do this. This gives the best flavor and preserves the acidity of the grenadine, but lacks texture and is not very stable.

Hot Method
Add equal parts pomegranate juice and sugar in a small saucepan. Heat until the sugar dissolves, but do not boil - 170 degrees F. is a good target. This method gives good flavor and some texture, and is fairly stable.

Hybrid Method
Add equal parts pomegranate juice and sugar in a medium saucepan. Over medium heat. cook until the mixture reduces by half. Let this mixture cool, then add an equal amount of fresh pomegranate juice to the syrup, and shake to combine.

Some people flavor their grenadine with various additives, ranging from orange flower water to pomegranate molasses to hibiscus flowers. As with all homemade syrups, a small amount of vodka can be used as a preservative.

From user admseattle comes a Paul Clarke recipe for homemade grenadine that uses pomegranate molasses instead of cooking down juice to a syrup:  

• 8 oz pomegranate juice
• 1 cup superfine sugar
• 2 oz pomegranate molasses
• 1 teaspoon orange flower water
• 1 oz vodka (to stabilize)

Mix pomegranate juice and sugar in a bottle or jar and shake until sugar is dissolved. Add the pomegranate molasses and shake well (it will dissolve faster if the juice is at room temperature); the molasses thickens and sweetens the syrup while lending a deeper, fruitier flavor. For an added flavor dimension, mix in a little orange flower water to taste. 
You can also add an ounce of vodka or grain alcohol as a preservative. Refrigerate and use within two weeks. You can freeze any extra for future use.