In this thesis computational studies on electromagnetic properties of metamaterials and applications are introduced. The studies include an introduction to the time-domain transmission line modelling (TLM) method and the fundamental scattering properties of metamaterials. The first major objective of the thesis is directed to predicting the resonant frequencies of some forms of cut-wire (CW) metamaterials by using approximate equivalent circuits. The second objective is the improvement of metamaterial simulation efficiency based on two approaches: a simulation method based on retrieved metamaterial electromagnetic properties and one based on digital filtering (DF) techniques. By using the DF techniques, metamaterials are effectively modelled and the simulation times are significantly reduced. The third objective is focused on studying CW metamaterial as potential absorbers by deliberately including conductive losses. The proposed CW metamaterials are found to exhibit customisable absorptance characteristics with arbitrary polarisation. This metamaterial absorber study includes an experimental validation.