Powder samples of Ag3LiIr2O6 and Ag3LiRu2O6 were synthesized from α-Li2IrO3 and Li2RuO3 respectively by ion exchange in an AgNO3 melt. The crystal structures of the title compounds were solved from high resolution laboratory X-ray powder diffraction (XRPD) patterns and from pair distribution function (PDF) analysis using synchrotron X-ray powder diffraction data. In both crystal structures edge sharing LiO6/3- and (Ir/Ru)O6/3-octahedra form honeycomb like layers that are stacked in a staggered fashion. Silver cations, situated in-between the layers mediate the interlayer interactions by linear O-Ag-O bonds. Anisotropic peak broadening in the XRPD patterns and diffuse scattering occurring as streaks in the precession electron diffraction (PED) patterns indicate the presence of stacking faults, which could be also visualized by high resolution transmission electron microscopy (HRTEM). Possible alternative stacking sequences were derived from the ideal crystal and incorporated into a microstructure model. By applying a supercell approach that randomly generates and averages stacking sequences based on transition probabilities and combining it with a grid search algorithm, the microstructures, i.e. the degrees of faulting in the structures of the title compounds were refined to the measured XRPD data. In result the crystal structures of Ag3LiIr2O6 and Ag3LiRu2O6 were found to be vastly faulted with almost no coherence of the stacked layers.