In Shakespeare's Hamlet, Polonius gives these words of advice to his son:
This above all: to thine own self be true,
And it must follow, as the night the day,
Thou canst not then be false to any man.
Farewell, my blessing season this in thee!
(Hamlet, Act I, Scene 3)
I think Shakespeare would agree with you here (or at least, Polonius). If one's honor is connected to truthfulness, genuineness, and authenticity, then "it must follow, as the night the day" that we are true to others if we are true to ourselves. In that way, when we honor ourselves, we also honor each other.