Critics who speak of Jane Austen as a liberal, in the same vein as they speak of Charlotte Brontë as a [literary] liberal, often refer to Mansfield Park for analysis, yet there are some identifiable elements of liberalism in Emma ["liberal" here opposes the idea of literary conservatism that Marilyn Butler and other critics of the 1970s Oxford school of literary criticism thought of as in keeping with the conservative literary establishment (canonical works) and Tory tradition (Blackwell].
Liberalism can be seen most sharply in Mr. Knightley's actions toward both Harriet Smith and Robert Martin. Though Robert Martin was a tenant farmer, Knightley genuinely respected and trusted him and assisted him in making a success of his farm. This was far more than lip-service because Knightly extended great personal and financial liberality to Martin, which some found at least surprising.
"His rank in society I would alter if I could, which is saying a great deal I assure you, Emma." (Knightley; Vol. III, Ch. XVIII)
Though Knightley discouraged Emma from trifling with Harriet as though she were a doll, he personally welcomed Harriet to visit the home of his brother and sister-in-law (Emma's elder sister) in London. In addition, at the ball, when Harriet was without a partner because Elton had been affronted by Emma's plan of marriage between him and Harriet, Knightley acted with great liberality by dancing--an entertainment he normally rejected--with Harriet himself (to her surprise and joy).
"Service! oh! it was such an inexpressible obligation!—The very recollection of it, and all that I felt at the time—when I saw him coming—his noble look—and my wretchedness before. Such a change! In one moment such a change! From perfect misery to perfect happiness!" (Harriet about Mr. Knightley, Vol. III, Ch. IV)
Liberality might also be seen in the theme Austen chose that some critics see in Marxist ideology as confronting the socio-economic issues that face unmarried gentlewomen who, by their place in society and by their education, have no opportunity to earn for themselves (except by the pen). This liberal socio-economic theme is elucidated by Beth Fowkes Tobin in "Aiding Impoverished Gentlewomen: Power and Class in Emma." Tobin asserts that Emma's social status and responsibilities position her among the power elite and that it was her responsibility, which she failed in, to provide for the impoverished gentlewomen in Emma. Emma's failure allows Austen to draw a liberal picture of a disempowering socio-economic issue of the era.
There is some difficulty in answering this question as asked, because the term "liberal" had a very different meaning in the early 19th century than it does now. The main political parties were the Whigs and Tories. Although some people would identify the Whigs as "liberals" the positions do not quite map onto modern uses of the term. The Whigs were generally a party of the urban industrialists, favouring religious freedom for dissenters, abolition of slavery, strengthening of the House of Commons (as opposed to Lords and the monarchy), and reduction or elimination of social safety nets. The Tories, strong supporters of the Church of England, tending towards monarchism, were drawn from the gentry, landowners, etc. and favoured tradition and charity.One could argue that in Emma, Austen was particularly concerned with the artificiality of class boundaries, and arguing in favour of social mobility based on innate virtues and talents as opposed to heredity.