In Part I of this paper, we have proposed the new concept of generalized voltage damping (GVD) and derived the system-wise GVD (sGVD) index for the global assessment of voltage stability and system strength. Part II of this paper extends this concept to develop a port-wise index for quantifying the voltage damping characteristics locally. To this end, we decompose the sGVD index into individual ports (or buses), thereby forming the port-wise GVD (pGVD) index, which can be computed using local measurements. By inheriting the interpretation of the system-wise index, we further prove that the average of pGVD indices across all ports is approximately identical to the sGVD index. Moreover, it exhibits favorable properties absent in existing indices based on the maximum Lyapunov exponents (MLEs) of terminal voltages, empowering its application as an assessment metric for the supportive capability of devices to short-term voltage stability. The model-independent feature enables the assessment considering the complex and nonlinear dynamics of inverter-based resources (IBRs) such as wind turbines, photovoltaics (PVs), and battery energy storages. Experimental simulations conducted on a heterogeneous IEEE 39-bus system and two practical power systems with massive renewable resource integration confirm the theoretical results. The influence of voltage control strategies of IBR, control parameters, integration locations, and active power control parameters are also analyzed, providing a new perspective for understanding the individual support of devices for short-term voltage stability.