The Collaborative International Dictionary of English v.0.48:

Judiciously \Ju*di"cious*ly\, adv.
   In a judicious manner; with good judgment; wisely.
   [1913 Webster]

WordNet (r) 3.0 (2006):

judiciously
    adv 1: in a judicious manner; "let's use these intelligence
           tests judiciously" [ant: injudiciously]

Moby Thesaurus II by Grady Ward, 1.0:

55 Moby Thesaurus words for "judiciously":
   artfully, astutely, calmly, cannily, carefully, cautiously,
   circumspectly, cleverly, composedly, conservatively, considerately,
   coolly, cunningly, discerningly, discreetly, dispassionately, easy,
   equably, evenly, gingerly, guardedly, heedfully, in balance,
   in moderation, in reason, intelligently, knowingly, mindfully,
   moderately, pawkily, providently, prudently, rationally,
   reasonably, regardfully, restrainedly, sagaciously, sensibly,
   serenely, shrewdly, smartly, soberly, soothingly, steadily,
   subduedly, temperately, thoughtfully, tranquilly, understandingly,
   wisely, with care, with caution, within bounds, within compass,
   within reason