Miss Maudie supports Atticus several different ways throughout the novel. In addition to passively declining to engage in conversations directed against Tom Robinson and the African American community, Maudie helps watch over Jem and Scout while Atticus works on his case. She watches the children as they play in her yard, sits on her porch with Scout in the evenings, and even bakes them cakes following the trial. After the trial is over, Miss Maudie continues to support Atticus by encouraging his children. She explains to Jem the importance of Atticus' job, which is to take a stand against ignorance. In Chapter 24, Miss Maudie also defends Atticus during Aunt Alexandra's missionary circle. Miss Maudie subtly chastises Mrs. Merriweather, who was indirectly criticizing Atticus for defending an African American.
While Miss Maudie may not out right say she supports Atticus, it is through interactions with his children that her support is shown. One of her biggest signs of respect, is how she tells Scout and Jem how their father is a rare person who is the same on the streets as he is in the home. This shows how she supports his personal integrity that many other people did not have.
When Tom Robinson dies, Miss Maudie talks to Jem and Scout:
. . . there are some men in this world who were born to do our unpleasant jobs for us. Your father's one of them . . . . We're so rarely called on to be Christians, but when we are, we've got men like Atticus to go for us.
This demonstrates her support of his moral strength and attitude. This is the specific reason he was chosen for this case. So, Miss Maudie shows her support of Atticus by affirming his actions and the man he is to his children.