  We present a calculation of the leading SU(3)-breaking
$\mathcal{O}(p^3)$-corrections to the electromagnetic moments and charge radius
(CR) of the lowest-lying decuplet resonances in covariant chiral perturbation
theory. In particular, the magnetic dipole moment (MDM) of the members of the
decuplet is predicted fixing the only low-energy constant (LEC) present up to
this order with the well measured MDM of the $\Omega^-$. We predict
$\mu_\Delta^{++}=6.04(13)$ and $\mu_\Delta^+=2.84(2)$ which agree well with the
current experimental information. For the electric quadrupole moment (EQM) and
the CR we use state-of-the-art lattice QCD results to determine the
corresponding LECs, whereas for the magnetic octupole moment (MOM) there is no
unknown LEC up to the order considered here and we obtain a pure prediction. We
compare our results with those reported in large $N_c$, lattice QCD,
heavy-baryon chiral perturbation theory and other models.
