I went to Tamburini, Trattoria Meloncello (Saturday night) and Antica Trattoria Gigina (Sunday lunchtime). Meloncello was full but Gigina had a few free tables.
Tamburini is not an all-round food emporium like eg. Harrods Food Halls. It sells cheese, hams, cakes and pasta. Its self-service canteen restaurant is cheap and the food is tasty. I particularly liked brussels sprouts that appeared to have been cooked in wine or vinegar.
Meloncello is sparsely yet more attractively decorated than Gigina. The ricotta in the tortelloni I had was superfresh- the dish was the outstanding one of my visit. At Gigina if you have booked your name will be on a welcome board when you arrive. I thought the food was good (especially at the price 25-30 per head euros all incl.)at both restaurants but according to two Italians I went with it was barely above average. These places both served traditional dishes. In retrospect I should have chosen at least one that served more inventive pasta dishes.