This work is a study of the effect of co-doping (ZrO2)0.9(Sc2O3)0.1 solid solution with yttria and/or ceria on the phase composition, local structure and transport properties of the crystals. The solid solution crystals were grown using directional melt crystallization in cold crucible. We show that ceria co-doping of the crystals does not stabilize the high-temperature cubic phase in the entire crystal bulk, unlike yttria co-doping. Ceria co-doping of the (ZrO2)0.9(Sc2O3)0.1 crystals increases their conductivity, whereas the addition of 1 mol.% yttria tangibly reduces the conductivity. Equimolar co-doping of the (ZrO2)0.9(Sc2O3)0.1 crystals with ceria and yttria changes the conductivity but slightly. Optical spectroscopy of the local structure of the crystals identified different types of optical centers. We found that the fraction of the trivalent cations having a vacancy in the first coordination sphere in the ceria co-doped crystals is smaller compared with that in the yttria co-doped crystals. Keywords: Single crystals, Solid oxide fuel cell, Solid solutions, Ionic conducting materials, ZrO2-Sc2O3-CeO2-Y2O3