Stromboli is best when had fresh, although cold stromboli is equally delectable. If you want to enjoy stromboli for a long time proper storage is essential. Store the stromboli in the fridge as soon as possible. Wrap it in aluminum foil or plastic wrap and store it in the fridge. You can also store it in a shallow airtight container. If you are looking at freezing stromboli, then wrap the stromboli in aluminum foil and store them in an airtight container in the freezer. You can also slice the stromboli and freeze the slices in portions.