This paper proposes an open-loop clock recovery circuit (CRC) using two high-Q dielectric resonator (DR) filters for 39.8 Gb/s and 42.8 Gb/s dual-mode operation. The DR filters are fabricated to obtain high Q-values of approximately 950 at the 40 GHz band and to suppress spurious resonant modes up to 45 GHz. The CRC is implemented in a compact module by integrating the DR filters with other circuits in the CRC. The peak-to-peak and RMS jitter values of the clock signals recovered from 39.8 Gb/s and 42.8 Gb/s pseudo-random binary sequence (PRBS) data with a word length of $2^{31}-1$ are less than 2.0 ps and 0.3 ps, respectively. The peak-to-peak amplitudes of the recovered clocks are quite stable and within the range of 2.5 V to 2.7 V, even when the input data signals vary from 150 mV to 500 mV. Error-free operation of the 40 Gb/s-class optical receiver with the dual-mode CRC is confirmed at both 39.8 Gb/s and 42.8 Gb/s data rates.