  We investigate the role of a specifically warped extra dimension in
constructing examples of higher dimensional spacetimes representing Lorentzian
wormholes. The warping chosen is largely inspired by the well-known non-static
Witten bubble of nothing, though our spacetimes are static and geometrically
different. Vacuum solutions in $D\geq 5$ dimensions and others
(non-asymptotically flat) with `perfectly normal' matter stress energy are
interpreted as possible Lorentzian wormholes. Asymptotically flat wormholes in
$D\geq 5$ with `exotic matter' and within this class of spacetimes also appear
to exist in all dimensions. A wormhole-black hole correspondence via double
Wick rotation is revisited and discussed. Finally, geodesic motion as well as
the behaviour of geodesic congruences, in the sub-class of five dimensional,
warped, vacuum wormhole spacetimes is also briefly analysed, with the aim of
obtaining characteristic properties and specific signatures which may help
improve our understanding of these geometries.
