Software-Implemented Hardware Fault Tolerance (SIHFT) techniques can be applied in processor-based systems, avoiding the modification of hardware components when designing dependable systems. These techniques allow the use of Commercial Off-The-Shelf (COTS) processors, but result in high overheads in terms of programs' code and performance. This paper presents a novel approach for designing reduced-overheads software-based fault-tolerant systems by using approximate computing at the software level. The approximate computing paradigm consists of improving energy and performance efficiency at the expense of accuracy in the results. Although the use of approximate computing has been previously proposed to reduce overheads of fault-tolerant systems, most of these works are focused on the hardware level, so the physical modification of the system is still mandatory, and thus, unfeasible in COTS components. Our proposal is validated by means of a case study using the Texas Instruments MSP430 microcontroller and several test programs, which are approximated and hardened using well-known techniques at the software level: loop perforation and SWIFT-R, respectively. Results show that it is possible to design dependable processor-based systems, with a significant reduction in overheads, in exchange for minor errors of accuracy.