K-Modulation in future high energy colliders

K-Modulation of the quadrupoles closest to the interaction point (IP) has been an indispensable tool to accurately measure the beta-function in the interaction point ($\beta^*$) in the Large Hadron Collider (LHC) at CERN. K-Modulation may become even more important to control the lower $\beta^*$ and reach the design luminosities in the High-Luminosity LHC (HL-LHC) and the Future Circular Collider (FCC). K-Modulation results also provide important input for the luminosity calibration and help in the identification and correction of errors in the machines. This paper presents a method for determining $\beta^*$ using K-Modulation adapted to the characteristic layout of both colliders. Using the latest models for the HL-LHC and the FCC-hh, estimated uncertainties on the measurements are presented. The results are compared to the accuracy of an alternative modulation scheme using a different powering scheme.