TAP Portugal has a deep discount fare at $138 one way for San Francisco to Rome via Lisbon. Round trip is a bit more at $329. This fare is currently available for departures about 4 days per week from January 20 to May 28. If you have 100 TP miles, the ticket price drops to $125 one way or $24 off a round trip ticket with 200 miles.
I received 200 TAP miles as a mileage program sign-up bonus last year. I also picked up 138 TAP miles with a hotel booking in Poland last summer.
For those who travel light with carry-on only, you can take advantage of the low one-way fare and simply stay in Lisbon for a ticket price quite a bit less than otherwise available from SFO.
TAP Portugal San Francisco SFO – Lisbon LIS – Rome FCO – LIS (21 hr overnight layover) – SFO
TAP Portugal SFO – LIS – FCO Rome one way
I like this last option for 22 hr 20 min layover in Lisbon as a really cheap two cities in one opportunity.