In composite Higgs and little Higgs models, the breaking of the electroweak symmetry is provided by a new, strongly-interacting sector. Apart from the physics of the Higgs boson and of possible top partners, these models are not very predictive, since the strongly-coupled regime starts just above the TeV scale. There is a unique opportunity to describe new "baryons" appearing above this scale as topological solitons of the low-energy theory. In QCD, skyrmions give a consistent picture of protons and neutrons purely in terms of the pion fields. Skyrmions appear in most little Higgs models, and their stability and mass in the range 10-100 TeV have important consequences for cosmology. They can be interesting dark matter candidates, but it is shown that the lightest skyrmion state is electrically charged in most existing models.