Johansson won 'Best Actress' for director Spike Jonze's Her and McConaughey took the 'Best Actor' prize for Dallas Buyers Club.
Her stars Joaquin Phoenix as Theodore Twombly, a writer who finds friendship in a newly-purchased operating system that is designed to meet his every need.
Johansson portrays Samantha, the voice behind the operating system.
Dallas Buyers Club tells the real-life story of Ron Woodroof (McConaughey), who began a drug smuggling operation after being diagnosed with HIV.
Both Johansson and McConaughey recently starred together in a commercial directed by Martin Scorsese for Dolce & Gabbana.
Her arrives in limited theaters on December 18 in the US, and will have a wide release on January 10 in the US and UK.
Meanwhile, Dallas Buyers Club is already playing in the US and will arrive in UK cinemas on February 7.
Watch a trailer of Dallas Buyers Club below: