  The observational possibilities enabled by an ultra-stable CODEX-like
spectrograph at the E-ELT will open new doors in the characterisation of the
nature of Dark Energy. Indeed, it will provide measurements of a so far
unexplored redshift-range ($2<z<5$) and will carry out simultaneously
cosmological tests such as the Sandage-Loeb test and precision tests of the
standard model. Here we will illustrate how, with these abilities, such
spectrographs - alone or in synergy with other facilities - will manage to
constrain cosmological scenarios and test classes of models that would
otherwise be difficult to distinguish from the standard $\Lambda{\rm CDM}$
paradigm.
