A requirement to reduce dependency on high-carbon fuels has resulted in the rapid advancement of electrochemical devices. Considerable research has been applied to improve device performance and lifetime in order to compete with incumbent technologies. Of the portfolio of electrochemical conversion technologies, solid oxide fuel cells (SOFC) offer high fuel versatility and fast reaction kinetics without the requirement of expensive catalysts. However, degradation due to high temperature operation limits cell performance and lifetime, impeding widespread commercialisation. Due to the inherent link between microstructure and electrochemical performance, many three-dimensional (3D) characterisation techniques have been employed in the pursuit of the mitigation of degradation through rational electrode design. Instruments such as lab-based X-ray microscopes are now capable of imaging across multiple length scales, where the highest resolutions (i.e. smallest voxel lengths) are comparable to specialist synchrotron facilities. A widely used metric to describe electrode microstructure is the triple-phase boundary (TPB); the location where reactions occur within the SOFC electrode. The total TPB length is a vital metric in assessing the quality of an SOFC material, and thus many efforts have been made to determine accurate values. In order to map the TPB locations in 3D, the three constituent phases: metal, ceramic, and pore, need to be distinguished and segmented, requiring high resolutions. Although TPB values have been reported and compared extensively in the literature, the influence of the microscopic roughness is yet to be investigated. Using X-ray computed tomography (CT), here, for the first time, the effect of resolution is inspected for several key microstructural parameters. Moreover, the study is extended through the use of multiple instruments for a variety of sample structures. This work introduces the importance of the fractal properties of structures characterised using X-ray CT, which we expect to be influential across a broad range of materials. The choice of resolution when characterising a structure is important and determined by a variety of factors: instrument, feature size, image quality, etc., and should ultimately be chosen in order to efficaciously expose the features under investigation, in addition to this, metrics extracted should only be directly compared at the same resolution and, if possible, should be inspected for fractal properties via a representative resolution analysis. These conclusions are not restricted to SOFCs but should be applied to all fields of microstructural analysis