The climax of Jane Austen's novel Emma can be found towards the ending chapters, namely chapter 45. It is the moment when, after a rough encounter with Mr. Knightley, she realizes that she has feelings for him after all.
However, all this occurs as a result of events that take place shortly before her emotional discovery.
We find Emma finding a way to save grace with the Bates after her odious behavior towards Miss Bates during the Box Hill gathering. During this gathering Emma insults Miss Bates when the latter laughs at herself saying that she could not come up with many clever ideas, and that instead she may be able to comply with at least three dull ideas. To this, Emma retorted with huge sarcasm:
Ah! ma’am, but there may be a difficulty. Pardon me, but you will be limited as to number—only three at once.
Basically, what Emma said to Miss Bates is that the latter is capable of coming up with more than plenty dull ideas and comments, and that it would be best to limit her before she starts.
This behavior leaves a really sad taste in Mr. Knightley who takes matters into his own hands and chastises Emma. This is the moment when Emma for once feels regrets about her actions.
After all this, in chapter 45, Emma explains how she tries to fix the situation with Miss Bates. During this exchange, Knightley understands Emma's behavior and sees kindness in her. She, equally, feels drawn to Knightley and they basically declare their love for each other when Knightley nearly kisses Emma's hand.
Every action after this specific event becomes the declining action of the plot which leads to the end. Therefore, the moment when Emma and Knighley declare or demonstrate their mutual attraction serves as the climax of the novel.