Today's reconfigurable hardware devices have huge densities and are partially reconfigurable, allowing for the configuration and execution of hardware tasks in a true multitasking manner. This makes reconfigurable platforms an ideal target for many modern embedded systems that combine high computation demands with dynamic task sets. A rather new line of research is engaged in the construction of operating systems for reconfigurable embedded platforms. Such an operating system provides a minimal programming model and a runtime system. The runtime system performs online task and resource management. In this paper, we first discuss design issues for reconfigurable hardware operating systems. Then, we focus on a runtime system for guarantee-based scheduling of hard real-time tasks. We formulate the scheduling problem for the 1D and 2D resource models and present two heuristics, the horizon and the stuffing technique, to tackle it. Simulation experiments conducted with synthetic workloads evaluate the performance and the runtime efficiency of the proposed schedulers. The scheduling performance for the 1D resource model is strongly dependent on the aspect ratios of the tasks. Compared to the 1D model, the 2D resource model is clearly superior. Finally, the runtime overhead of the scheduling algorithms is shown to be acceptably low.