Antonyms of unintelligibly:
clearly, intelligibly, understandably.
Examples of usage:
  1. I explained to Mr. Montenero to what circumstances I had so unintelligibly alluded.
    "Tales & Novels, Vol. IX [Contents: Harrington; Thoughts on Bores; Ormond]", Maria Edgeworth.
  2. My three sailors were like statues, Phillippi muttering unintelligibly.
    "Mr. Trunnell", T. Jenkins Hains.
  3. A few birds began to chirp; but, as Susan was listening to them, her mother started in her sleep, and spoke unintelligibly.
    "The Parent's Assistant", Maria Edgeworth.