Fault mitigation techniques based on pure software, known as software-implemented hardware fault tolerance (SIHFT), are very attractive for use in COTS (commercial off-the-shelf) microprocessors because they do not require physical modification of the system. However, these techniques cause software overheads that may affect the efficiency and costs of the overall system. This paper presents a design method of radiation-induced fault-tolerant microprocessor-based systems with lower execution time overheads. For this purpose, approximate computing and selective fault mitigation software-based techniques are used; thus it can be used in COTS devices. The proposal is validated through a case study for the TI MSP430 microcontroller. Results show that the designer can choose among a wide spectrum of design configurations, exploring different trade-offs between reliability, performance, and accuracy of results.