Limits on large moons of extrasolar planets, when combined with observations of the Solar System, allow tests of models of planet and moon formation, migration and structure. Unfortunately, if the host stars of transiting planets, one of the most promising places to search for moons, are spotted, effects such as spot crossing events and long term photometric trends make moon detection challenging. Consequently we extend current moon detection methods, in particular the scatter in the folded light-curve method, to allow its use for spotted stars, by excising the planetary transit and fitting the photometric trends. We present and discuss robust exo-moon radius thresholds calculated for one planet and one planet candidate, both with highly spotted host stars, using archived Kepler transiting planet data. For the case of HAT-P 11 b we can rule out moons with radii less than 0.9 Earth radii and for KOI 1353.01 moons with 2% of the host star's radius. This work demonstrates that detection of Earth-sized, and super Earth-sized moons of transiting planets is feasible, even when the host star is highly spotted.