Extremal Optimisation (EO) is a recent nature-inspired meta-heuristic whose search method is especially suitable to solve combinatorial optimisation problems. This paper presents the implementation of a multi-objective version of EO to solve the real-world Radio Frequency IDentification (RFID) antenna design problem, which must maximise efficiency and minimise resonant frequency. The approach we take produces novel modified meander line antenna designs. Another important contribution of this work is the incorporation of an inseparable fitness evaluation technique to perform the fitness evaluation of the components of solutions. This is due to the use of the NEC evaluation suite, which works as a black box process. When the results are compared with those generated by previous implementations based on Ant Colony Optimisation (ACO) and Differential Evolution (DE), it is evident that our approach is able to obtain competitive results, especially in the generation of antennas with high efficiency. These results indicate that our approach is able to perform well on this problem; however, these results can still be improved, as demonstrated through a manual local search process.