We consider the semiclassical limit of nonlinear Schr\"odinger equations with
wavepacket initial data. We recover the Wigner measure of the problem, a
macroscopic phase-space density which controls the propagation of the physical
observables such as mass, energy and momentum. Wigner measures have been used
to create effective models for wave propagation in random media, quantum
molecular dynamics, mean field limits, and the propagation of electrons in
graphene. In nonlinear settings, the Vlasov-type equations obtained for the
Wigner measure are often ill-posed on the physically interesting spaces of
initial data. In this paper we are able to select the measure-valued solution
of the 1+1 dimensional Vlasov-Poisson equation which correctly captures the
semiclassical limit, thus finally resolving the non-uniqueness in the seminal
result of [Zhang, Zheng \& Mauser, Comm. Pure Appl. Math. (2002) 55,
doi:10.1002/cpa.3017]. The same approach is also applied to the
Vlasov-Dirac-Benney equation with small wavepacket initial data, extending
several known results