We employ the adaptive resolution approach AdResS, in its recently developed Grand Canonical-like version (GC-AdResS) [H. Wang, C. Hartmann, C. Schütte, and L. Delle Site, Phys. Rev. X 3, 011018 (2013)], to calculate the excess chemical potential, μ(ex), of various liquids and mixtures. We compare our results with those obtained from full atomistic simulations using the technique of thermodynamic integration and show a satisfactory agreement. In GC-AdResS, the procedure to calculate μ(ex) corresponds to the process of standard initial equilibration of the system; this implies that, independently of the specific aim of the study, μ(ex), for each molecular species, is automatically calculated every time a GC-AdResS simulation is performed.