This study investigates several important considerations to be made when optimising the structural aspects of a single-degree-of-freedom (SDOF) electromagnetic vibration energy harvester. Using the critically damped stress method, the damping and power output of the harvester were modelled and verified, displaying an excellent agreement with the experimental results. The SDOF harvester was structurally optimised under a certain set of constraints and it was found that under the fixed beam's thickness condition, the harvester displayed an insignificant increase in power output as a function of volume when the device's size was relatively larger. This highlights the importance of considering a smaller practical volume for this case. Additionally, when optimising the device using a low stress constraint and a low damping material, it was observed that considering the load resistance as an input parameter to the objective function would lead to a higher power output compared to the optimum load resistance condition. Further analysis indicated that there exists a power limit when the electromagnetic coupling coefficient approaches infinity. For the case of a high electromagnetic coupling coefficient value and a small volume constraint, it is possible to achieve approximately 80.0% of the harvester's power limit. Finally, it was demonstrated that a high power output can be achieved for a SDOF electromagnetic harvester by considering a high-density proof mass centred at the free end of the beam.