Textile reinforced concrete is becoming increasingly important in construction. Besides the application in new constructions, textile reinforcement can be used for the strengthening of plain and reinforced concrete structures in the form of fabric reinforced cementitious matrices (FRCMs). An effective and promising application of FRCMs is the confinement of RC columns. Even though great research efforts have been carried out recently, there are still some discrepancies in current prediction models. This paper presents an extensive experimental study on concrete compression members confined with carbon fabric reinforced cementitious matrices (CFRCMs). The experimental program consists of specimens with varying geometries, concrete strengths, and strengthening systems. The investigations showed the importance of a precise determination of the FRCM’s material parameters. Furthermore, possible reductions of the FRCMs tensile strength due to the application in curved areas have to be taken into account. Finally, an empirical prediction model as well as recommendations for the experimental determination of the strengthening systems material properties and reduction factors is presented.