  We study non-linear sigma models whose target spaces are the Higgs phases of
supersymmetric SO and USp gauge theories by using the Kahler and hyper-Kahler
quotient constructions. We obtain the explicit Kahler potentials and develop an
expansion formula to make use of the obtained potentials from which we also
calculate the curvatures of the manifolds. The 1/2 BPS lumps in the U(1) x SO
and U(1) x USp Kahler quotients and their effective descriptions are also
studied. In this connection, a general relation between moduli spaces of
vortices and lumps is discussed. We find a new singular limit of the lumps with
non-vanishing sizes in addition to the ordinary small lump singularity. The
former is due to the existence of singular submanifolds in the target spaces.
