The Collaborative International Dictionary of English v.0.48:

Honorably \Hon"or*a*bly\, adv.
   1. In an honorable manner; in a manner showing, or consistent
      with, honor.
      [1913 Webster]

            The reverend abbot . . . honorably received him.
                                                  --Shak.
      [1913 Webster]

            Why did I not more honorably starve?  --Dryden.
      [1913 Webster]

   2. Decently; becomingly. [Obs.] "Do this message honorably."
      --Shak.

   Syn: Magnanimously; generously; nobly; worthily; justly;
        equitably; fairly; reputably. Honorarium

WordNet (r) 3.0 (2006):

honorably
    adv 1: in an honorable manner; "he acted honorably" [syn:
           honorably, uprightly] [ant: dishonorably]
    2: with honor; "he was honorably discharged after many years of
       service" [syn: honorably, honourably] [ant:
       dishonorably]

Moby Thesaurus II by Grady Ward, 1.0:

27 Moby Thesaurus words for "honorably":
   blamelessly, conscientiously, creditably, decently, erectly,
   estimably, fastidiously, high-mindedly, honestly, immaculately,
   irreproachably, meticulously, morally, nobly, punctiliously,
   purely, reputably, respectably, righteously, scrupulously,
   stainlessly, unimpeachably, unspottedly, uprightly, upstandingly,
   virtuously, worthily