  The discovery of a 125 GeV Higgs boson and rising lower bounds on the masses
of superpartners have lead to concerns that supersymmetric models are now fine
tuned. Large stop masses, required for a 125 GeV Higgs, feed into the
electroweak symmetry breaking conditions through renormalisation group
equations forcing one to fine tune these parameters to obtain the correct
electroweak vacuum expectation value. Nonetheless this fine tuning depends
crucially on our assumptions about the supersymmetry breaking scale. At the
same time $U(1)$ extensions provide the most compelling solution to the
$\mu$-problem, which is also a naturalness issue, and allow the tree level
Higgs mass to be raised substantially above $M_Z$. These very well motivated
supersymmetric models predict a new $Z'$ boson which could be discovered at the
LHC and the naturalness of the model requires that the $Z'$ boson mass should
not be too far above the TeV scale. Moreover this fine tuning appears at the
tree level, making it less dependent on assumptions about the supersymmetry
breaking mechanism. Here we study this fine tuning for several $U(1)$
supersymmetric extensions of the Standard Model and compare it to the situation
in the MSSM where the most direct tree level fine tuning can be probed through
chargino mass limits. We show that future LHC $Z'$ searches are extremely
important for challenging the most natural scenarios in these models.
