Honor is one of the central conundrums in Julius Caesar. Some actions are done in the name of honor, others in spite of it. National honor challenges personal honor, and obligations and desires put honor at stake. All these layers of honor, which often conflict with each other, ultimately lead back to the issue of perspective. Each character has to decide what's best for him and act on it accordingly. In the end, they can only do honor to their own judgment, as they have no clear standard for what is good in their world.
Antony is not dishonorable; all he does is avenge the death of Caesar. Just as the conspirators thought their murder was excused by their honorable intention, Antony uses dishonorable means to restore honor to Rome.
Brutus is the play's most honorable character. He sacrifices himself for the state, accepts his punishment nobly, and chooses to take his own life rather than return to Rome in chains. He stays true to his own ideals and values from the beginning to the bitter end.