  Stupendously large black holes exceeding $10^{11} M_\odot$ could exist,
supported by recent observations of unexpectedly massive black holes at high
redshifts. These objects may constitute a part of dark matter or even dark
energy. One possibility to explain the cosmic accelerated expansion could be to
consider charged black holes whose mutual repulsion overcomes their
gravitational attraction. However, the extreme charge required turns these
black holes into naked singularities, whose existence is questioned by the
cosmic censorship hypothesis. Since the latter is driven by theoretical
assumptions, we work out the most promising observables which are least
cosmology-dependent to test their existence. We derive the electro-magnetic and
gravitational lensing effects caused by such extreme objects at distances much
larger than their extent to investigate possible ways for a discovery.
Restricting searches to black holes between $10^{12}$ to $10^{14} M_\odot$, we
show that such objects do not cause totally disruptive catastrophes, like
dissociation of neutral hydrogen clouds or proton decay induced by strong
electro-magnetic fields. Einstein rings of the order of 10" and rotation
measures of plasma clouds subject to the magnetic fields induced by the moving
black holes are identified as optimum observable signatures for now. Future
space-based black-hole telescopes will follow up on these candidates and
finally check the cosmic censorship hypothesis by their strong-field
strong-lensing signatures, like an additional sub-arcsecond inner Einstein
ring. Observable effects are so surprisingly moderate that a violation of
cosmic censorship is hard to detect and even explaining cosmic expansion with
moving naked singularities might be possible.
