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This study investigates the damping properties of Cu–Al–Mn shape memory alloys (SMAs) with various chemical compositions and the effects of the addition of quaternary alloying elements Ag and Nb on the microstructure, martensitic transformation behavior, and damping capacity of SMAs. Compared to other Cu–12Al– x Mn (x = 4–7 wt%) SMAs, Cu–12Al–5Mn has a more significant inherent and intrinsic internal friction (IF PT + IF I) peak above room temperature. The addition of Ag or Nb to Cu–12Al–5Mn reduced the grain size, thereby increasing the hardness of the alloys; however, the damping capacity and temperature of the IF PT + IF I peak decreased simultaneously. The addition of Ag to Cu–12Al–5Mn significantly reduced the damping capacity (IF PT +IF I peak) because of the notable decrease in the amount of transformed martensite. Moreover, the addition of Nb to Cu–12Al–5Mn caused the AlNb 3 phase to precipitate, limiting the mobility of the martensite variant interfaces and slightly decreasing the damping capacity (IF PT + IF I peak). Among the Ag- and Nb-doped Cu–12Al–5Mn SMAs, Cu–12Al–5Mn–1 Nb showed not only a significantly higher hardness but also a higher IF PT + IF I peak, with tan δ exceeding 0.01 at approximately 50 °C. [Display omitted] • In Cu-based SMAs, damping capacity depends on microstructure and the volume fraction of the transformed martensite. • Alloying elements with different mechanisms affect the damping performance of Cu-based SMAs. • In Cu-based SMAs, both damping capacity and mechanical strength improve by optimizing chemical composition. [ABSTRACT FROM AUTHOR]