The Collaborative International Dictionary of English v.0.48:

Court \Court\, v. t. [imp. & p. p. Courted; p. pr. & vb. n.
   Courting.]
   1. To endeavor to gain the favor of by attention or flattery;
      to try to ingratiate one's self with.
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            By one person, hovever, Portland was still
            assiduously courted.                  --Macaulay.
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   2. To endeavor to gain the affections of; to seek in
      marriage; to woo.
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            If either of you both love Katharina . . .
            Leave shall you have to court her at your pleasure.
                                                  --Shak.
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   3. To attempt to gain; to solicit; to seek.
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            They might almost seem to have courted the crown of
            martyrdom.                            --Prescott.
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            Guilt and misery . . . court privacy and solitude.
                                                  --De Quincey.
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   4. To invite by attractions; to allure; to attract.
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            A well-worn pathway courted us
            To one green wicket in a privet hedge. --Tennyson.
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WordNet (r) 3.0 (2006):

courting
    n 1: a man's courting of a woman; seeking the affections of a
         woman (usually with the hope of marriage); "its was a brief
         and intense courtship" [syn: courtship, wooing,
         courting, suit]