The Collaborative International Dictionary of English v.0.48:

Resolutely \Res"o*lute*ly\, adv.
   In a resolute manner; with fixed purpose; boldly; firmly;
   steadily; with perseverance.
   [1913 Webster]

         Some . . . facts he examines, some he resolutely
         denies.                                  --Swift.
   [1913 Webster]

WordNet (r) 3.0 (2006):

resolutely
    adv 1: showing firm determination or purpose; "she resolutely
           refused to look at him or speak to him"; "he entered the
           building resolutely" [ant: irresolutely]
    2: with firmness; "`I will come along,' she said decisively"
       [syn: decisively, resolutely] [ant: indecisively]

Moby Thesaurus II by Grady Ward, 1.0:

93 Moby Thesaurus words for "resolutely":
   assiduously, audaciously, bec et ongles, boldly, bravely,
   bulldoggishly, chivalrously, committedly, courageously, daringly,
   decidedly, decisively, determinedly, devotedly, diligently,
   doggedly, doughtily, earnestly, faithfully, fearlessly, firmly,
   fixedly, gallantly, gamely, gutsily, hammer and tongs, hardily,
   heart and soul, heroically, in all seriousness, in earnest,
   in good earnest, indefatigably, industriously, inflexibly,
   insistently, intrepidly, knightly, like a bulldog, like a leech,
   like a man, like a soldier, loyally, obstinately, patiently,
   perseveringly, persistently, persistingly, pertinaciously,
   ploddingly, pluckily, purposefully, relentlessly, resolvedly,
   sedulously, seriously, sincerely, singlemindedly, sloggingly,
   spunkily, stalwartly, staunchly, steadfastly, steadily, stoutly,
   tenaciously, tirelessly, tooth and nail, unabatingly,
   unfalteringly, unfearfully, unfearingly, unflaggingly,
   unflinchingly, unintermittingly, uninterruptedly, unrelentingly,
   unremittingly, unrestingly, unsleepingly, unswervingly, untiringly,
   unwaveringly, unwearyingly, unyieldingly, valiantly, valorously,
   wearilessly, wholeheartedly, with a will, with constancy,
   with total dedication, yeomanly