There is no such thing as “conduction of electric wave in conductor” (and I am unsure about where “electric waves” can be observed). There is a conduction of electric current in a conductor. One can say that electric potential in a piece of conductor is always the same (so the electric field is zero inside it), although it is not always so due to resistance, and generally the concept of electric potential is rather foggy; see Ambiguity on the notion of potential in electrical circuits? for discussion. An electric wire or other device made of conductor can guide a wave, but such wave can propagate only due to presence of a dielectric (vacuum included). Thick shields made of a conductor, instead, are used to completely suppress (reflect and partially absorb) incoming E/M radiation in an appropriate frequency range.
In a (non-vacuum) dielectric, both electric and magnetic fields can exist, so an electromagnetic wave can propagate, although not exactly in the same way as in vacuum due to effects of permeability (electric, and possibly magnetic).