  We study resonant tunneling through a layered medium with a negative index
medium (NIM) slab as a constituent layer. We demonstrate large delays in
transmission mediated by the surface and the guided modes of the structure with
low losses. We show how important it is to include NIM dispersion for correct
assessment of the nature and magnitude of the delay. We also point out the role
of NIM absorption for the feasibility of such compact delay devices.
