Caroenum is barely mentioned in ancient texts, which makes identifying its true nature particularly difficult. We know that it is a grape syrup, made by reducing grape juice/must. According to Grainger and Dalby, it is reduced by 1/3 to 1/2. They also believe that it was made from white grape juice, and that its purpose was to add 'bulk' to a meal, rather than to flavour it; this task falls to passum and defrutum instead. Caroenum is also used to make 'oenogarum', a 'vinaigrette' made by mixing fish sauce, oil, wine, and spices.
Caroenum is sweet, but not sickeningly so. It is a touch thicker than standard white grape juice.
This is something you make at home rather than buy in the shops; as long as you can find a carton of white grape juice, you're set. To make it, pour as much grape juice as you need into a pan and boil until it has reduced by 1/3 to 1/2. Using a pan with a wide base is recommended, as this will speed up the process of evaporation. Once it has cooled, bottle it up for future use.
If needs be you can just use white grape juice - this will provide sweetness and 'bulk', albeit not as pronounced as with caroenum.