We present a study on the discoverability of temporarily captured orbiters (TCOs) by present day or near-term anticipated ground-based and space-based facilities. TCOs (Granvik, M., Vaubaillon, J., Jedicke, R. . Icarus 218, 262-277) are potential targets for spacecraft rendezvous or human exploration (Chyba, M., Patterson, G., Picot, G., Granvik, M., Jedicke, R., Vaubaillon, J. . J. Indust. Manage. Optim. 10, 477-501) and provide an opportunity to study the population of the smallest asteroids in the Solar System. We find that present day ground-based optical surveys such as Pan-STARRS and ATLAS can discover the largest TCOs over years of operation. A targeted survey conducted with the Subaru telescope can discover TCOs in the 0.5-1.0 m diameter size range in about 5 nights of observing. Furthermore, we discuss the application of space-based infrared surveys, such as NEOWISE, and ground-based meteor detection systems such as CAMS, CAMO and ASGARD in discovering TCOs. These systems can detect TCOs but at a uninteresting rate. Finally, we discuss the application of bi-static radar at Arecibo and Green Bank to discover TCOs. Our radar simulations are strongly dependent on the rotation rate distribution of the smallest asteroids but with an optimistic distribution we find that these systems have >80% chance of detecting a >10 cm diameter TCO in about 40 h of operation.