The transient response of an induction coil above an infinite conducting plate is calculated in the time domain (TD) by combining a semi-analytical modal expansion approach with the Euler integration scheme. The derived state equation at a given time step is formally equivalent to the Helmholtz equation with an imaginary frequency linked to the sampling rate, which provides a significant computational advantage with respect to spectral methods based on Fourier/Laplace domain discretization. In addition, time stepping schemes prove to be more robust than the spectral approaches, where the optimal choice of the sample frequencies is an issue of major concern. The developed solution is applied for the calculation of the magnetic field in a driver–pickup coil inspection configuration involving pulsed currents, and the coil response is obtained using the TD version of the reciprocity theorem. The theoretical results are compared against reference numerical solutions demonstrating an excellent agreement.