Wire + Arc Additive Manufacturing (WAAM) has been widely attempted in producing large metal components and the research on monitoring wire quality in the wire feeding process is of significant importance to the quality of the final product. In this thesis, electromagnetic sensing technique for real-time inspection of wire conductivity is applied to WAAM process for the first time. In this research, a strategy for non-contact measurement of the conductivity of metal wires used in Wire + Arc Additive Manufacture (WAAM) is proposed. A cylindrical magnetic sensor consisting of coil pair (a transmitting and a receiving coil) is designed and the change in the mutual impedance due to the presence of the wire inside the sensor is measured at multiple frequencies. It was found that the phase of the impedance (calculated from real/imaginary parts) of the coils is linearly related to the conductivity of the wire measured via a contact four-terminal measurement method. Moreover, single-frequency and multi-frequency measurements are compared and different calibration approaches using ferrite and transformer are developed to optimize the calibration process. This technique can be potentially applied to the real-time and in-situ inspection of metal wires by measuring their conductivity variation, which could help in the quality control of Wire + Arc Additive Manufacture processes. In addition, an analytical solution based on Dodd and Deeds formulas is proposed to evaluate the relationship between wire sample conductivity/ radius and impedance/inductance.