In computational electromagnetics (EM), the accuracy of the numerical simulation is compromised by randomness which may arise in various forms such as electric parameters and input sources. Though EM problems are usually treated as deterministic, there exist many instances where some input parameters of EM simulators cannot be strictly determined due to limited knowledge regarding these parameters. The ambiguity of input parameters causes a degree of uncertainty in the responses of the system. In order to gain an understanding of the reliability of numerical simulations, the possible uncertainty together with the system response can be investigated. This thesis aims at quantifying the uncertainty of the finite-difference time-domain (FDTD) simulation induced by the uncertainty of input parameters, which is known as forward uncertainty quantification (UQ) or the uncertainty propagation problem. The Monte Carlo method (MCM) is the traditional technique utilised in UQ, yet it requires a considerable number of FDTD simulations, leading to excessive computational resources. In order to reduce the computational cost of UQ for the FDTD simulation, a series of UQ techniques, such as the stochastic collocation method and the non-intrusive polynomial chaos (NIPC) expansion method, have been investigated. In comparison to other UQ techniques, the NIPC method demonstrates high accuracy and computational efficiency. However, this method suffers from the curse of dimensionality whereby the number of required FDTD simulations grows substantially when the number of uncertain parameters increases. To lift the curse of dimensionality, the sparse schemes including the hyperbolic scheme and the least angle regression (LARS) method were also studied. Furthermore, this thesis investigated machine learning techniques for UQ. An artificial neural network based UQ method was proposed to quantify the uncertainty of the FDTD response. This method builds a surrogate model for the 11 FDTD simulation, and thus bypassing the thousands of system-runs required in the MCM. The proposed method has the potential to significantly reduce the computational cost of UQ, which could be of significant use within the bioelectromagnetics field.