This paper presents a novel design of a coprocessor that performs hardware-accelerated task scheduling for embedded real-time systems consisting of mixed-criticality real-time tasks. The proposed solution is based on the Robust Earliest Deadline (RED) algorithm and previously developed hardware architectures used for scheduling of real-time tasks. Thanks to the HW implementation of the scheduler in the form of a coprocessor, the scheduler operations (i.e., instructions) are always completed in two clock cycles regardless of the actual or even maximum task amount within the system. The proposed scheduler was verified using simplified version of UVM and applying billions of randomly generated instructions as inputs to the scheduler. Chip area costs are evaluated by synthesis for Intel FPGA Cyclone V and for 28-nm TSMC ASIC. Three versions of real-time task schedulers were compared: EDF-based scheduler designed for hard real-time tasks only, GED-based scheduler and the proposed RED-based scheduler, which is suitable for tasks of various criticalities. According to the synthesis results, the RED-based scheduler consumes LUTs and occupies larger chip area than the original EDF-based scheduler with equivalent parameters used. However, the RED-based scheduler handles variations of task execution times better, achieves higher CPU utilization and can be used for the scheduling of hard real-time, soft real-time and nonreal-time tasks combined in one system, which is not possible with the former algorithms.