We report on the development and application of a brand-new contactless method based on eddy currents with a view to designing a generic apparatus for the characterization of some transport properties of a large range of semiconductors. The eddy current probe, constituted of a coil connected to a transmission line, interacts with the semiconductor wafer under inspection. The innovative approach of this work consists in measuring the impedance of the coil by reflectometry using a broadband multicarrier test signal, i.e. containing multiple frequencies. An electromagnetic model of the coil-wafer interaction is then used to estimate the conductivity of the wafer. This process results in a new contactless conductivity measurement system that exhibits a very wide conductivity measurement range and allows the characterization of a large variety of semiconductor materials. The device is also very fast potentially allowing the measurement of transport properties of semiconductors in fast transient conditions. As a practical example, the performance of our device is demonstrated by estimating the conductivity of a set of crystalline silicon wafers.