Two circuit modelling and parameterisation techniques for optimisation of a left-handed microstrip transmission line for antenna applications are presented. Such a transmission line is characterised by high transmission loss ripples in the required frequency band, which hinders its use as a wideband feeding network in antenna array applications. The first circuit modelling technique is based on numerical parameterisation, whereas the second is based on analytical parameterisation. The goal of the parameterisation is to obtain multivariable functions to represent the components of the circuit model with the geometrical dimensions as parameters. A novel and improved circuit model taking into consideration the external mutual coupling between the elements of the left handed transmission line was used to optimise its performance in terms of absolute transmission loss and minimum ripple over a wide frequency band. The performance of the improved equivalent circuit model is compared with the electromagnetic simulations, and a good agreement is obtained. A prototype of the optimised left-handed transmission line was built and tested. Satisfactory agreement was obtained between the simulated and measurement results.