Universities in England could face fines under new legislation if they fail to protect free speech on campus.
Visiting speakers, academics or students could seek compensation if they suffer loss from a breach of a university's free speech obligations.
The Higher Education (Freedom of Speech Bill) was one of the proposed pieces of legislation announced in the Queen's Speech on Tuesday.
Universities said it was important not to create "unnecessary bureaucracy".
Under the plans, new freedom of speech and academic duties would be placed on universities and, for the first time, on student unions.
Individuals would be given a right to seek compensation through the courts if the freedom of speech duties of an institution or student union had been breached.
The Office for Students, the higher education watchdog in England, would have the power to impose fines on institutions if they breached the rules.
Among the proposals there is also an appointed "free speech champion" who would examine potential infringements of duties, for example, the no-platforming of speakers or the dismissal of academics.
The government hopes the changes will ensure that university staff feel safe to put forward controversial or unpopular views, without being at risk of losing their jobs.
But a spokeswoman for Universities UK (UUK) said: "Universities are (rightly) already legally required to have a code of practice on free speech and to update this regularly.
"It is important that the Higher Education (Freedom of Speech) Bill is proportionate by focusing on the small number of incidents, while not duplicating existing legislation and creating unnecessary bureaucracy for universities which could have unintended consequences."
Jo Grady, head of the University and College Union, said: "There are serious threats to freedom of speech and academic freedom from campus, but they come from the government and university managers, not staff and students.
"Widespread precarious employment strips academics of the ability to speak and research freely, and curtails chances for career development.
"If the government wants to strengthen freedom of speech and academic freedom, it shouldn't be policing what can and cannot be said on campus, and encourage university managers to move staff on to secure, permanent contracts."
But Education Secretary Gavin Williamson said it was a basic human right "to be able to express ourselves freely and take part in rigorous debate".
"Our legal system allows us to articulate views which others may disagree with as long as they don't meet the threshold of hate speech or inciting violence - this must be defended, nowhere more so than within our world-renowned universities.
"Holding universities to account on the importance of freedom of speech in higher education is a milestone moment in fulfilling our manifesto commitment, protecting the rights of students and academics, and countering the chilling effect of censorship on campus once and for all."
Universities minister Michelle Donelan added: "This bill will ensure universities not only protect free speech but promote it too.
"After all how can we expect society to progress or for opinions to modernise unless we can challenge the status quo?"