Observational strategies for varying constants with ESPRESSO and
  ELT-HIRES
  The observational evidence for the acceleration of the universe demonstrates
that canonical theories of cosmology and particle physics are incomplete, if
not incorrect. Several few-sigma hints of new physics, discussed in this
workshop, are arguably smoke without a smoking gun. Forthcoming high-resolution
ultra-stable spectrographs will play a crucial role in this quest for new
physics, by enabling a new generation of precision consistency tests. Here we
focus on astrophysical tests of the stability of nature's fundamental
couplings, discussing the improvements that can be expected with ESPRESSO and
ELT-HIRES and their impact on fundamental cosmology. We find that the current
E-ELT configuration has the potential to constrain dark energy more strongly
than standard surveys with thousands of low-redshift ($z<2$) supernovas.
