The Collaborative International Dictionary of English v.0.48:

Quoif \Quoif\ (kwoif or koif), n. & v. t.
   See Coif. --Shak.
   [1913 Webster]

The Collaborative International Dictionary of English v.0.48:

Coif \Coif\ (koif or kw[aum]f), n. [OF. coife, F. coiffe, LL.
   cofea, cuphia, fr. OHG. kuppa, kuppha, miter, perh. fr. L.
   cupa tub. See Cup, n.; but cf. also Cop, Cuff the
   article of dress, Quoif, n.]
   1. A cap. Specifically:
      (a) A close-fitting cap covering the sides of the head,
          like a small hood without a cape.
      (b) An official headdress, such as that worn by certain
          judges in England. [Written also quoif.]
          [1913 Webster]

                From point and saucy ermine down
                To the plain coif and russet gown. --H. Brocke.
          [1913 Webster]

                The judges, . . . althout they are not of the
                first magnitude, nor need be of the degree of
                the coif, yet are they considerable. --Bacon.
          [1913 Webster]

   2. a coiffure.
      [PJC]