Summary: The Bartnik mass is a notion of quasi-local mass which is remarkably difficult to compute. C. Mantoulidis and R. Schoen [Classical Quantum Gravity 32, No. 20, Article ID 205002, 16 p. (2015; Zbl 1326.83051)] developed a novel technique to construct asymptotically flat extensions of minimal Bartnik data in such a way that the ADM mass of these extensions is well-controlled, and thus, they were able to compute the Bartnik mass for minimal spheres satisfying a stability condition. In this work, we develop extensions and gluing tools, à la Mantoulidis-Schoen, for time-symmetric initial data sets for the Einstein-Maxwell equations that allow us to compute the value of an ad-hoc notion of charged Barnik mass for suitable charged minimal Bartnik data.