Satellites of extrasolar planets, or exomoons, are on the frontier of detectability using current technologies and theoretical constraints should be considered in their search. Motivated by this, we determine theoretical constraints of orbital stability through numerical N-body simulations. We simulate systems of exomoons and submoons for 105 planetary orbits, while considering different initial orbital phases to obtain the critical semimajor axis in terms of RH,p or the host satellite’s Hill radius RH,sat , respectively. We find that, assuming circular coplanar orbits, the stability limit for an exomoon is 0.40 RH,p and for a submoon is 0.33 RH,sat. Additionally, we evaluate the observational feasibility of detecting these satellites through photometric, radial velocity, or direct imaging observations using the Neptune-sized exomoon candidate Kepler 1625b-I and identify how stability can shape the identification of future candidates. Lastly, we apply theoretical constraints of orbital stability and tidal migration to the six candidate Kepler Object of Interest (KOI) systems proposed by Fox & Wiegert to identify whether these systems can potentially host exomoons.