She protested her innocence with dignity.

Literal

She [topic-は] dignity [object-を] holding self [topic-は] not-guilty [quotative-と] protested.

威厳をもって ('with dignity') is the adverbial frame — もって is the て-form of もつ used here adverbially to mean 'with, by means of.' 自分は無罪だ is direct quotation of her assertion: 'I am innocent,' with the と quotative wrapping it for 抗議する ('protest'). 無罪 ('not guilty') is the legal/courtroom term, a binary against 有罪 ('guilty') — the word slots the scene into a judicial register even without other courtroom language.