  We show that certain classes of contact 3-manifolds do not admit
non-separating contact type embeddings into any closed symplectic 4-manifolds,
e.g. this is the case for all contact manifolds that are (partially) planar or
have Giroux torsion. The latter implies that manifolds with Giroux torsion do
not admit contact type embeddings into any closed symplectic 4-manifolds.
Similarly, there are symplectic 4-manifolds that can admit smoothly embedded
non-separating hypersurfaces, but not of contact type: we observe that this is
the case for all symplectic ruled surfaces.
