  Non-Abelian BPS vortex solutions are constructed in N=2 theories with gauge
groups SO(N)\times U(1). The model has N_f flavors of chiral multiplets in the
vector representation of SO(N), and we consider a color-flavor locked vacuum in
which the gauge symmetry is completely broken, leaving a global SO(N)_{C+F}
diagonal symmetry unbroken. Individual vortices break this symmetry, acquiring
continuous non-Abelian orientational moduli. By embedding this model in
high-energy theories with a hierarchical symmetry breaking pattern such as
SO(N+2) --> SO(N)\times U(1) --> 1, the correspondence between non-Abelian
monopoles and vortices can be established through homotopy maps and flux
matching, generalizing the known results in SU(N) theories. We find some
interesting hints about the dual (non-Abelian) transformation properties among
the monopoles.
