In the context of hybrid passive vibration control, the effectiveness of the Tuned Liquid Column Damper (TLCD) for seismic protection of base-isolated (BI) systems has been demonstrated both numerically and experimentally. In contrast to the previous studies on TLCDs, the present study explores the possibility of equipping a BI system with a sliding model of TLCD (STLCD), until now introduced only for the suppression of wind-induced vibrations of fixed-base structures. Specifically, the proposed STLCD consists of a U-shaped tank partially filled with water, mounted on a roller support and connected to the BI system via a spring-dashpot system. The validity of the introduced mathematical model is assessed by means of an extensive shaking table testing campaign at the Laboratory of Experimental Dynamics at the University of Palermo, Italy. For the experimental tests, a small-scale model of a single-degree-of-freedom (SDOF) BI structure with the STLCD is constructed, and the effectiveness of the proposed combined control strategy is experimentally evaluated. Finally, comparisons with traditional TLCDs and TMDs are made and the control efficiency is discussed with emphasis on the reduction of the accelerations of the BI system.