The idea of Jane Austen as a conservative--morally, as a political Tory and as part of the male literary tradition--comes from the 1975 critical publication by Marilyn Butler, Jane Austen and the War of Ideas. In it Butler asserts that Austen is following in the footsteps of traditional English Literary cannon and is "programmatically conservative" instead of a "non-partisan liberal moralist." Subsequent criticism in Feminism, especially by Showalter and Gilbert, disputes Butler's early opinion, yet echoes of "conservative" still can be heard.
Emma is one that most easily accepts the mantle of conservative because the deep level, underlying story seems to be: incompetent female has foolish pursuits that result in difficulties for everyone and must be sorted out by strong, sensible patriarchal male figure. This deep level story seems to be reinforced and symbolized by Harriet's encounter with gypsies from which she is rescued by Frank Churchill (one of the least dependable of the males and yet a bona fide representative of male patriarchy).
[Harriet's] terror and her purse were too tempting, and she was followed, or rather surrounded, by the whole gang, demanding more.
In this state Frank Churchill had found her, she trembling....
Another predominantly mentioned element indicating conservatism for Austen is the marriage scenarios of the narrative.  Sensible, reserved Jane Fairfax yields to pressure from impetuous, undependable though patriarchal Frank Churchill to consent to a secret engagement resulting in great psychological distress for Jane.  Emma marries the heroic patriarchal figure Mr. Knightly who has never ceased to correct and scold (though lovingly) Emma from the outset of the narrative.  Harriet's ignoble birth is, after all, when all is said and done, considered a social impediment to friendship with Emma, thus Harriet marries Farmer Martin and Emma bestows her blessing and adieu.