If you don’t have enough pomodorini to hang, another option is to store them loosely. They will last longer if some of the stem is left attached. If the stem is missing, storing them with the stem side down will help to prolong storage life. As with other root cellar crops, check them frequently and consume as they ripen.
From Cook’s Illustrated, “How to prolong the shelf life of a tomato”:
We’ve heard that storing a tomato with its stem end facing down can prolong shelf life. To test this theory, we placed one batch of tomatoes stem-end up and another stem-end down and stored them at room temperature. A week later, nearly all the stem-down tomatoes remained in perfect condition, while the stem-up tomatoes had shriveled and started to mold. Why the difference? We surmised that the scar left on the tomato skin where the stem once grew provides both an escape for moisture and an entry point for mold and bacteria. Placing a tomato stem-end down blocks air from entering and moisture from exiting the scar. To confirm this theory, we ran another test, this time comparing tomatoes stored stem-end down with another batch stored stem-end up, but with a piece of tape sealing off their scars. The taped, stem-end-up tomatoes survived just as well as the stem-end-down batch.