It is now recognized that the purely elastomeric and frictional bearings cannot provide effective vertical seismic isolation of a framed structure due to their high vertical frequency. Amplification of vertical acceleration along the building height is documented in the near-fault area. Moving resonance effects in the vertical direction are also expected due to shifting of the dominant vibration periods related to the nonlinear behaviour of both the superstructure and base-isolation system. New seismic isolation systems able to carry the gravity loads with relatively low vertical stiffness have been proposed, but the calibration of the vertical isolation ratio remains elusive. The main objective of this work is to evaluate the isolation ratio in the vertical direction required for effective protection against the vertical component of near-fault ground motions. To achieve this, the horizontal and vertical base-isolation is applied to a six-storey pavilion of the hospital campus in Cosenza (Italy). An in-series vertical assembly of a high-damping rubber bearing (HDRB) and a high-damping rubber layer (HDRL), the latter independent of the horizontal and vertical (in tension) responses of the HDRB, is adopted. Design properties of the HDRBs are evaluated in line with provisions of the European seismic codes, while thickness of the HDRLs corresponds to eight values of the vertical-to-horizontal stiffness ratio used for the base-isolated test structures. A purpose-built C++ code adopts a lumped plasticity model for RC frame members and coupling of the horizontal and vertical motions, change of the critical buckling load due to significant horizontal displacement and cavitation for the HDRBs. A purpose-built Matlab code is implemented to investigate effects of the time-varying structural response on the vertical seismic isolation, using the continuous wavelet transforms in combination with the complex Morlet wavelet. Elastic and inelastic dynamic time-history analyses are carried out in order to calibrate results of the wavelet analysis, considering two sets of fifteen near-fault earthquakes with non-pulse-type and pulse-type behaviour in the vertical direction. It is concluded that wavelet analysis represents a useful and simplified tool for an optimal selection of the vertical isolation ratio, requiring only results of elastic dynamic analysis of the test structure.