The spin-lattice relaxation time has been studied trough alternating-current susceptometry and ultralow-frequency Raman spectroscopy in a family of silver(II)-derived molecular systems with spin 1/2 and formulas [AgII(m-CTH)(NO3)2] (1) and [AgII(m-CTH)(ClO4)2] (2), where CTH = meso-5,5,7,12,12,14-hexamethyl-1,4,8,11-tetraazacyclotetradecane. The combination of both techniques demonstrates the occurrence of slow spin magnetic relaxation induced by spin-phonon interaction. The magnetic behavior of these silver(II)-derived systems opens the door to a new cation in the scarce family of S = 1/2 systems with slow relaxation of magnetization.