  Charge-$4e$ superconductivity as a novel phase of matter remains elusive so
far. Here we show that charge-$4e$ phase can arise as a vestigial order above
the nematic superconducting transition temperature in time-reversal-invariant
nematic superconductors. On the one hand, the nontrivial topological defect --
nematic vortex -- is energetically favored over the superconducting phase
vortex when the nematic stiffness is less than the superfluid stiffness;
consequently the charge-$4e$ phase emerges by proliferation of nematic vortices
upon increasing temperatures. On the other hand, the Ginzburg-Landau theory of
the nematic superconductors has two distinct decoupling channels to either
charge-$4e$ orders or nematic orders; by analyzing the competition between the
effective mass of the charge-$4e$ order and the cubic potential of the nematic
order, we find a sizable regime where the charge-$4e$ order is favored. These
two analysis consistently show that nematic superconductors can provide a
promising route to realize charge-$4e$ phases, which may apply to candidate
nematic superconductors such as PbTaSe$_2$ and twisted bilayer graphene.
