We combine several numerical and semi-analytical methods to study the $5d$ double perovskites Sr2YIRO6 and Ba2YIRO6 which were recently proposed to exhibit excitonic magnetism. Starting from the density functional theory and constrained random phase approximation we construct effective multi-band Hubbard models. These are analyzed by means of static and dynamical mean-field theories and strong coupling expansion. We find both materials to be insulators, but, contrary to the experimental claims, with a large spin gap of several hundreds meV preventing formation of an ordered state at low temperature