  It is proved that no wormholes can be formed in viable scalar-tensor models
of dark energy admitting its phantom-like ($w < -1$) behaviour in cosmology,
even in the presence of electric or magnetic fields, if the non-minimal
coupling function $f(\Phi)$ is everywhere positive and the scalar field $\Phi$
itself is not a ghost. Some special static, spherically symmetric wormhole
solutions may exist if $f(\Phi)$ is allowed to reach zero or to become
negative, so that the effective gravitational constant becomes negative in some
region making the graviton a ghost. If $f$ remains non-negative, such solutions
require severe fine tuning and a very peculiar kind of model. If $f < 0$ is
allowed, it is argued (and confirmed by previous investigations) that such
solutions are generically unstable under non-static perturbations, the
instability appearing right near transition surfaces to negative $f$.
