In this short review, we provide some new insights into the material synthesis and characterization of modern multi-component superconducting oxides. Two different approaches such as the high-pressure, high-temperature method and ceramic combinatorial chemistry will be reported with application to several typical examples. First, we highlight the key role of the extreme conditions in the growth of Fe-based superconductors, where a careful control of the composition-structure relation is vital for understanding the microscopic physics. The availability of high-quality LnFeAsO (Ln = lanthanide) single crystals with substitution of O by F, Sm by Th, Fe by Co, and As by P allowed us to measure intrinsic and anisotropic superconducting properties such as Hc2, Jc. Furthermore, we demonstrate that combinatorial ceramic chemistry is an efficient way to search for new superconducting compounds. A single-sample synthesis concept based on multi-element ceramic mixtures can produce a variety of local products. Such a system needs local probe analyses and separation techniques to identify compounds of interest. We present the results obtained from random mixtures of Ca, Sr, Ba, La, Zr, Pb, Tl, Y, Bi, and Cu oxides reacted at different conditions. By adding Zr but removing Tl, Y, and Bi, the bulk state superconductivity got enhanced up to about 122 K
