We report on the experimental investigation of potential high-performance cavity length stabilization using odd-indexed higher-order spatial modes. Schemes based on higher-order modes are particularly useful for micro-cavities that are used for enhanced fluorescence detection of a few emitters, which need to minimize photons leaking from a stabilization beam. We describe the design and construction of an assembly for a microcavity setup with tunable high passive stability. In addition, different types of active stabilization techniques based on higher-order modes are then implemented and characterized based on their performance. We achieved a stability of about 0.5 pm rms, while the error photons leaking from the continuous locking beam to a fluorescence detector are suppressed by more than 100-fold. We expect these results to be important for quantum technology implementations of various emitter-cavity setups, where these techniques provide a useful tool to meet the highly challenging demands.