Ramón Meña had the following finishes at major championships – 1987 Pan-American Games: 57.0 kg. Greco-Roman (2nd); 1991 Pan-American Games: 52.0 kg. Greco-Roman (2nd); 1995 Pan-American Games: 57.0 kg. Greco-Roman (4th).
| Games | Discipline (Sport) / Event | NOC / Team | Pos | Medal | As | |
|---|---|---|---|---|---|---|
| 1988 Summer Olympics | Wrestling | Ramón Mena | ||||
| Bantamweight, Greco-Roman, Men (Olympic) | =17 | |||||
| Bantamweight, Freestyle, Men (Olympic) | =19 | |||||
| 1992 Summer Olympics | Wrestling | Ramón Mena | ||||
| Flyweight, Greco-Roman, Men (Olympic) | =11 |