The Collaborative International Dictionary of English v.0.48:

Narrowly \Nar"row*ly\, adv. [AS. nearulice.]
   1. With little breadth; in a narrow manner.
      [1913 Webster]

   2. Without much extent; contractedly.
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   3. With minute scrutiny; closely; as, to look or watch
      narrowly; to search narrowly.
      [1913 Webster]

   4. With a little margin or space; by a small distance; hence,
      closely; hardly; barely; only just; -- often with
      reference to an avoided danger or misfortune; as, he
      narrowly escaped.
      [1913 Webster]

   5. Sparingly; parsimoniously.
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   6. With close adherence to the literal meaning of a text; as,
      to interpret narrowly; to construe narrowly; to read
      narrowly; -- used especially of laws and contracts.
      [PJC]

WordNet (r) 3.0 (2006):

narrowly
    adv 1: in a narrow manner; not allowing for exceptions; "he
           interprets the law narrowly" [ant: broadly, broadly
           speaking, generally, loosely]