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The detection and characterization of the exomoon population would open the door to a new field within exoplanetary science. We present the prospects for the James Webb and the Nancy Grace Roman Space Telescopes (JWST & Roman) to detect exomoons transiting isolated planetary-mass objects (IPMOs—also known as free-floating planets). Given the high occurrence and close orbits of solar system moons, transiting exomoons are likely to occur around 10%-15% of IPMOs, although the intrinsic variability of the IPMO may make detections challenging. For at least 30 of the currently known nearby IPMOs, observations of a single transit with JWST would allow for the detection of an Io-or Titan-sized moon. Beyond JWST, we propose that a Transiting Exosatellites, Moons & Planets in Orion (TEMPO) survey with Roman could monitor hundreds of IPMOs and brown dwarfs in the Orion Nebula Cluster for transits …