  The calculated nuclear matrix elements for the neutrinoless double-beta
($0\nu\beta\beta$) decay suffer from several limitations. Predicted
matrix-element values depend on the many-body method used to calculate them
and, in addition, they may need to be "quenched", albeit by an unknown amount
due to the relatively high momentum transferred in the decay. These
uncertainties are hard to figure out from theoretical calculations alone
because of the unique character of $0\nu\beta\beta$ decay, not clearly related
to other nuclear structure observables. We present recent progress in the
determination of the nuclear matrix elements. First, we report improved shell
model calculations in an extended configuration space of two harmonic
oscillator shells. Second, we note the relation between the $0\nu\beta\beta$
decay and double Gamow-Teller transitions that can in principle be measured in
double charge-exchange reactions. These new insights pave the way for a more
reliable estimation of the value of the nuclear matrix elements.
