Silicon carbide (SiC) components are being considered for a wide range of nuclear applications due to their high-temperature strength retention, low neutron absorption, chemical inertness, and dimensional stability under neutron irradiation. However, machining and joining of SiC components have traditionally limited its application to relatively simple geometries. Recent work has demonstrated additive manufacturing of complex, high-purity, crystalline SiC components using a combination of binder jet printing and densification via chemical vapor infiltration (CVI). The process lends itself to embedding of fuel, absorbers, moderators, and sensors at strategic locations within a component. The latter could allow for enhanced in situ performance monitoring of limiting fuel temperatures, self-shielded neutron flux, and potentially spatially distributed strain within complex SiC components if sensors can be successfully embedded during CVI. This work describes (1) methods for embedding sensors; (2) thermodynamic analyses and material compatibility testing for identifying sensors capable of surviving high temperatures and exposure to hydrogen and hydrogen chloride during CVI; and (3) nuclear applications for embedded sensors, including potential failure modes during fabrication and during reactor operation. Molybdenum-sheathed thermocouples were successfully embedded in a complex SiC component, whereas niobium-sheathed high-temperature irradiation-resistant thermocouples started to drift as soon as the reactant gases were introduced and ultimately failed during CVI due to severe constrained expansion, potentially resulting from niobium hydride formation in the low-temperature region of the CVI system. Optical fibers were successfully embedded in SiC, but further work is needed to protect the fragile fiber leads after their protective coatings are removed during CVI.