Marlena Valles and Rebecca Meredith claim they were met with boos and calls of "shame" as they spoke in favour of female equality during Glasgow University Union's (GUU) annual Ancients competition.
The women claimed they were also met with comments about their appearance and choice of outfit.
Ms Meredith, from Kilmacolm, Inverclyde, who is studying politics at Cambridge, described misogynist and intimidating behaviour from a small number of men in the chamber.
The Cambridge Union Society, the debating club of Cambridge University, yesterday unanimously voted to revoke reciprocal membership with the GUU and will no longer send debaters to the Ancients contest.
The GUU was formed in 1880s but did not allow women to join until 1980, making it the last union in the UK to have single-sex membership.
Past members include Donald Dewar, John Smith, Sir Menzies Campbell and Charles Kennedy.
GUU president David Lockhart, who chaired the final, issued a full apology to Ms Valles and Ms Meredith. Disciplinary action, ranging from financial penalties to suspension from the union, may also be taken against the culprits.
Ms Meredith wrote on Facebook: "The amazing Marlena Valles and I were openly booed by a small number of misogynistic male Glasgow Union debaters and members during the final of the Glasgow Ancients competition for our presence as female speakers.
"Sexist comments were made about our appearance, and we were told to 'get that woman out my union' by a male member. Our speeches were interrupted by cries of 'shame woman', and boos at mention of female equality."
Organisers describe the chamber at GUU as both "infamous and intimidating" but Ms Meredith said she had never been treated in such a way during a debate.
She added: "I have been told as a female debater that I should be careful not to sound 'hysterical', but never have I been openly disparaged in a final merely for being a woman."
Ms Valles, a law student at Edinburgh University, said: "It is difficult to speak confidently to an audience that is booing you for the sole reason that you are a woman in a dress."
Mr Lockhart said: "GUU believes in providing an experience for members and visitors, based on inclusivity, fairness and respect. It is clear that displays of behaviour that are misogynistic or sexist are entirely incompatible with these values."