A packaged component may include an interposer and integrated circuit dies mounted on the interposer. At least one of the dies may be a radiation-hardened integrated circuit die, whereas the remaining dies may be non-radiation-hardened dies. If desired, the interposer may be a radiation-hardened interposer whereas the integrated circuit dies may be non-radiation-hardened dies. The radiation-hardened die or the radiation-hardened interposer may include monitor circuitry that is used to test non-radiation-hardened circuitry of the packaged component. Test results may be stored in a database at the monitor circuitry or transmitted to external devices such as a server. The monitor circuitry may be used to reconfigure failed circuitry or may control multiplexing circuitry in the interposer to functionally replace the failed circuitry. If desired, the monitor circuitry may adjust power consumption of non-radiation-hardened circuitry based on the test results.