The Collaborative International Dictionary of English v.0.48:

Burnish \Bur"nish\, v. i.
   To shine forth; to brighten; to become smooth and glossy, as
   from swelling or filling out; hence, to grow large.
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         A slender poet must have time to grow,
         And spread and burnish as his brothers do. --Dryden.
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         My thoughts began to burnish, sprout, and swell.
                                                  --Herbert.
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The Collaborative International Dictionary of English v.0.48:

Burnish \Bur"nish\, n.
   The effect of burnishing; gloss; brightness; luster.
   --Crashaw.
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The Collaborative International Dictionary of English v.0.48:

Burnish \Bur"nish\, v. t. [imp. & p. p. Burnished; p. pr. &
   vb. n. Burnishing.] [OE. burnischen, burnissen, burnen, OF.
   burnir, brunir, to make brown, polish, F. brunir, fr. F. brun
   brown, fr. OHG. br?n; cf. MHG. briunen to make brown, polish.
   See Brown, a.]
   To cause to shine; to make smooth and bright; to polish;
   specifically, to polish by rubbing with something hard and
   smooth; as, to burnish brass or paper.
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         The frame of burnished steel, that east a glare
         From far, and seemed to thaw the freezing air.
                                                  --Dryden.
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         Now the village windows blaze,
         Burnished by the setting sun.            --Cunningham.
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   Burnishing machine, a machine for smoothing and polishing
      by compression, as in making paper collars.
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Moby Thesaurus II by Grady Ward, 1.0:

22 Moby Thesaurus words for "burnish":
   buff, dress, finish, furbish, glance, glaze, gloss, luster, polish,
   rub, rub up, sand, sandblast, sandpaper, scour, shine, sleek,
   slick, slick down, smooth, varnish, wax