This paper presents a dual-modular-redundancy and dual-level error-interception based triple-node-upset (TNU) tolerant latch design (namely DDETT) for safety-critical applications. The DDETT latch comprises two parallel single-node-upset self-recoverable cells to store values and three C-elements to intercept errors. Both of the two cells are constructed from triple mutually-feeding-back 2-input C-elements, and the cells feed two internal C-elements for first-level error-interception. Moreover, the two internal C-elements feed an output-stage C-element for second-level error-interception, making the DDETT latch TNU-tolerant in that it can tolerate any possible TNU. This paper further presents a low-cost version of the DDETT latch, namely LCDDETT. The LCDDETT latch uses two dual-interlocked-storage-cells (DICEs) to store values and uses dual-level error-interception to tolerate any possible TNU with cost-effectiveness. Simulation results not only confirm the TNU-tolerance of the proposed latches but also demonstrate that the delay-power-area products of the DDETT and LCDDETT latches are reduced by approximately 34% and 58%, respectively.