Sant'Eufemia is tucked inside the Archbishop's Palace courtyard just above the Piazza del Duomo, and it is one of the finest Romanesque interiors in Umbria. The 12th-century church is built on the site of the Lombard ducal palace, incorporating earlier structures, and its interior has a clarity and simplicity that the more famous Duomo below lacks.
The three-aisled nave, the carved capitals, and the matroneum (upper women's gallery) preserved on the north side are all in excellent condition. It is a small church, and you can absorb it in half an hour, but you are likely to find yourself sitting quietly for longer. The Diocesan Museum next door holds Lippi's original triptych from the Duomo, worth seeing alongside the architecture.