The prediction of the transverse wall beam impedance at the first unstable betatron line (8kHz) of the CERN Large Hadron Collider (LHC) is of paramount importance for understanding and controlling the related coupled-bunch instabilities. Until now only novel analytical formulas were available at this frequency. Recently, laboratory measurements and numerical simulations were performed to cross-check the analytical predictions. The experimental results based on the measurement of the variation of a probe coil inductance in the presence of (i)sample graphite plates, (ii)stand-alone LHC collimator jaws, and (iii)a full LHC collimator assembly are presented in detail. The measurement results are compared to both analytical theories and simulations. In addition, the consequences for the understanding of the LHC impedance are discussed. © 2009 The American Physical Society.