We have developed a concurrent method of optical measurements using optical fiber bundles and charge coupled devices (CCDs), especially equipped for application to combinatorial samples. This approach can also be used for experiments performed at cryogenic temperatures. This combinatorial characterization method will be explained in detail. The dependence of the optical properties in combinatorial samples of ZnO/(Mg,Zn)O multi-quantum wells prepared by laser molecular-beam epitaxy upon well width was found to be smooth compared with the samples grown by a conventional method. The use of lattice-matched ScAlMgO4 substrates greatly improved the properties of quantum wells and, as a result, a bright photoluminescence (PL) of free excitons could be observed even at room temperature. In addition, the PL could be tuned in the energy range 3.3-3.6 eV by choosing the appropriate barrier height and well layer thickness.