The Swans have never made the FA Cup final but they have reached the semis twice: in 1926 against Bolton, and in 1964 against Preston.
You can read more about these games here: FA Cup semi 1926 FA Cup semi 1964
The Swans have, however, been to Wembley four times to date. These occasions have been the 1994 League Trophy (sponsored by Autoglass) final, where Swansea beat Huddersfield on penalties; the Division 3 play-off final in 1997, where Swansea lost narrowly to Northampton Town; the victorious Football League Championship play-off final of 2011, when Reading were despatched 4-2; and the 2012 the Capital One Cup final
-
- Northampton Town v Swansea City Play Off final Div 3 1997
Wembley 2011
100 Years of Swansea City FC 
Pingback: Swans at Wembley? | 100 Years of Swansea City FC