  Excited states exhibiting double excitation character are notoriously
difficult to model using conventional single-reference methods, such as
adiabatic time-dependent density-functional theory (TD-DFT) or
equation-of-motion coupled cluster (EOM-CC). In the present work, we provide
accurate reference excitation energies for transitions involving a substantial
amount of double excitation using a series of increasingly large
diffuse-containing atomic basis sets. Our set gathers 20 vertical transitions
from 14 small- and medium-size molecule. Depending on the size of the molecule,
selected configuration interaction (sCI) and/or multiconfigurational
calculations are performed in order to obtain reliable estimates of the
vertical transition energies. In addition, coupled cluster approaches including
at least contributions from iterative triples are assessed. Our results clearly
evidence that the error in CC methods is intimately related to the amount of
double excitation character of the transition. For "pure" double excitations
(i.e. for transitions which do not mix with single excitations), the error in
CC3 can easily reach 1 eV, while it goes down to few tenths of an eV for more
common transitions (like in \emph{trans}-butadiene) involving a significant
amount of singles. As expected, CC approaches including quadruples yield highly
accurate results for any type of transitions. The quality of the excitation
energies obtained with multiconfigurational methods is harder to predict. We
have found that the overall accuracy of these methods is highly dependent of
both the system and the selected active space. The inclusion of the $\sigma$
and $\sigma^*$ orbitals in the active space, even for transitions involving
mostly $\pi$ and $\pi^*$ orbitals, is mandatory in order to reach high
accuracy. A theoretical best estimate (TBE) is reported for each transition.
