  We present a new class of solutions for static spherically symmetric wormhole
spacetimes in conformal gravity and outline a detailed method for their
construction. As an explicit example, we construct a class of traversable and
non-traversable wormholes that are locally conformal to Schwarzschild-(anti) de
Sitter spacetimes. These wormhole spacetimes are exact vacuum solutions in, but
not being limited to, Weyl gravity and conformal scalar-tensor theories.
Importantly, the method implies that every conformal theory of gravity with
static spherically symmetric solutions will trivially contain wormholes without
the need for exotic matter. Applying those results on gravitational theories
that possess conformal symmetry in the ultraviolet regime, the central
singularities of black holes can be replaced with wormhole throats. We
speculate on possible phenomenological consequences. We also discuss the
inclusion of matter fields and give explicit examples of charged wormholes in
Weyl gravity and conformal scalar-tensor gravity.
