Since modern propulsion systems are insufficient for large-scale space exploration, a breakthrough in propulsion physics is required. Amongst different concepts, the EMDrive is a proposed device claiming to be more efficient in converting energy into propulsive forces than classical photon momentum exchange. It is based on a microwave resonator inside a tapered cavity. Recently, Taylor suggested using a laser instead of microwaves to boost thrust by many orders of magnitude due to the higher quality factor of optical resonators. His analysis was based on the theory of quantised inertia by McCulloch, who predicted that an asymmetry in mass surrounding the device and/or geometry is responsible for EMDrive-like forces. We put this concept to the test in a number of different configurations using various asymmetrical laser resonators, reflective cavities of different materials and size as well as fiber-optic loops, which were symmetrically and asymmetrically shaped. A dedicated high precision thrust balance was developed to test all these concepts with a sensitivity better than pure photon thrust, which is the force equivalent to the radiation pressure of a laser for the same power that is used to operate each individual devices. In summary, all devices showed no net thrust within our resolution at the Nanonewton range, meaning that any anomalous thrust must be below state-of-the-art propellantless propulsion. This puts strong limits on all proposed theories like quantised inertia by at least 4 orders of magnitude for the laboratory-scale geometries and power levels used with worst case assumptions for the theoretical predictions.