  We discuss observational constrains coming from supernovae Ia imposed on the
behaviour of the Randall-Sundrum models. In the case of dust matter on the
brane, the difference between the best-fit Perlmutter model with a
$\Lambda$-term and the best-fit brane models becomes detectable for redshifts
$z > 1.2$. It is interesting that brane models predict brighter galaxies for
such redshifts which is in agreement with the measurement of the $z = 1.7$
supernova. We also demonstrate that the fit to supernovae data can also be
obtained, if we admit the "super-negative" dark energy (phantom matter) $p= -
(4/3) \varrho$ on the brane, where the dark energy in a way mimics the
influence of the cosmological constant. It also appears that the dark energy
enlarges the age of the universe which is demanded in cosmology. Finally, we
propose to check for dark radiation and brane tension by the application of the
angular diameter of galaxies minimum value test. We point out the existence of
coincidence problem for the brane tension parameter.
