  We show that the James Webb Space Telescope will be able to detect dwarf
satellites of high-$z$ Lyman Break Galaxies (LBGs). To this aim, we use
cosmological simulations following the evolution of a typical
$M_\star\simeq10^{10}\rm M_\odot$ LBG up to $z\simeq6$, and analyse the
observational properties of its five satellite dwarf galaxies ($10^7{\rm
M_\odot}<M_\star<10^9{\rm M_\odot}$). Modelling their stellar emission and dust
attenuation, we reconstruct their rest-frame UV-optical spectra for $6<z<6.5$.
JWST/NIRCam synthetic images show that the satellites can be spatially resolved
from their host, and their emission is detectable by planned deep surveys.
Moreover, we build synthetic spectral energy distributions and colour-magnitude
diagrams for the satellites. We conclude that the color $\rm F200W-F356W$ is a
powerful diagnostic tool for understanding their physical properties once they
have been identified. For example, $\rm F200W-F356W~\lesssim-0.25$ can be used
to identify star-bursting ($\rm SFR\sim5~M_\odot yr^{-1}$), low-mass
($M_\star\lesssim5\times 10^8\rm M_\odot$) systems, with $\sim80\%$ of their
stars being young and metal-poor ($\log(Z_\star/Z_\odot) < -0.5$).
