  Macroscopic traversable wormhole solutions to Einstein's field equations in
$(2+1)$ and $(3+1)$ dimensions with a cosmological constant are investigated.
Ensuring traversability severely constrains the material used to generate the
wormhole's spacetime curvature. Although the presence of a cosmological
constant modifies to some extent the type of matter permitted (for example it
is possible to have a positive energy density for the material threading the
throat of the wormhole in $(2+1)$ dimensions), the material must still be
``exotic'', that is matter with a larger radial tension than total mass-energy
density multiplied by $c^2$. Two specific solutions are applied to the general
cases and a partial stability analysis of a $(2+1)$ dimensional solution is
explored.
