Ceramic materials have found their way into a multitude of technical fields such as medical implants, spaceflight, electronics and sensorics in the form of high-performance components. This is due to their unique combination of structural and functional properties, such as hardness, density, strength or electrical and thermal conductivity. In the process of material development for such components, strength testing is an essential tool to characterise the structural material behaviour and to assess the development process. Additionally, the knowledge of the material's strength and its underlying scatter allows the prediction of the failure of brittle components and an estimation of the expected lifetime in service. Since ceramic materials differ significantly from other material classes, a variety of testing methods have been specifically developed for ceramics over the past 50 years. The goal of this work was to develop and improve existing methods for strength testing. This was done for a selection of biaxial bending tests and, depending on the individual testing method, was accomplished on different levels for each method. For the Ball-on-Ring-test, the mathematical description of the stress- and deflection-field was completely reworked and validated through Finite-Element-Analysis. For the Ball-on-Three-Balls-test, the evaluation of the maximum tensile stress was simplified significantly and extended to allow the evaluation of square plates. Furthermore, the influence non-linear, load-dependent effects on the measured strength was analysed and included in the current evaluation. These findings were validated not just through simulations, but also through experimental data obtained through X-ray tomography. Additionally, the comparability of the Ball-on-Three-Balls-test to other testing methods was made possible through providing the numerical data for the effective volume and surface on an open-access scale. The application of this data was demonstrated by a comparison of the Ball-on-Three-Balls-test to the Ring-on-Ring-test. Alongside this comparison, the influence of friction-reducing intermediate layers for the Ring-on-Ring-test was discussed and the influence of uneven surfaces on the measured strength was investigated. Another focus of this work was set on strength testing of additively manufactured ceramic specimens or components. During fabrication, process- and orientation- specific, periodic structures are created on the surface of each component, which cause stress concentrations and subsequently affect the failure behaviour significantly. Additionally, the maximum component size is restricted for most manufacturing processes, so that the necessary amount of specimens for statistical strength analysis cannot be fabricated within a single print-job. In order to consider these aspects appropriately, a novel testing method was developed in cooperation with the IKTS Dresden. Within this work, a detailed theoretical analysis of the testing method and possible sources of error was performed, and the results were put into perspective and validated through experimental work.