  We obtain a closed system of equations for scalar perturbations in a
multi-component braneworld. Our braneworld possesses a phantom-like equation of
state at late times, $w_{\rm eff} < -1$, but no big-rip future singularity. In
addition to matter and radiation, the braneworld possesses a new effective
degree of freedom - the 'Weyl fluid' or 'dark radiation'. Setting initial
conditions on super-Hubble spatial scales at the epoch of radiation domination,
we evolve perturbations of radiation, pressureless matter and the Weyl fluid
until the present epoch. We observe a gradual decrease in the amplitude of the
Weyl-fluid perturbations after Hubble-radius crossing, which results in a
negligible effect of the Weyl fluid on the evolution of matter perturbations on
spatial scales relevant for structure formation. Consequently, the quasi-static
approximation of Koyama and Maartens provides a good fit to the exact results
during the matter-dominated epoch. We find that the late-time growth of density
perturbations on the brane proceeds at a faster rate than in $\Lambda$CDM.
Additionally, the gravitational potentials $\Phi$ and $\Psi$ evolve differently
on the brane than in $\Lambda$CDM, for which $\Phi = \Psi$. On the brane, by
contrast, the ratio $\Phi/\Psi$ exceeds unity during the late matter-dominated
epoch ($z \lesssim 50$). These features emerge as "smoking gun" tests of
phantom brane cosmology and allow predictions of this scenario to be tested
against observations of galaxy clustering and large-scale structure.
