The magnetic properties of the double perovskite ruthenate compounds with general composition Sr_YRu___Ir_O_ (x=0, 0.1, 0.2, 0.3) were studied in the temperature range of 2-300 K by means of measurements of magnetic susceptibility, specific heat, and thermal conductivity. Polycrystalline samples were prepared by solid-state reaction. Sr_YRuO_ (Sr-2116) is an antiferromagnetic (AFM) insulator, derived from the parent compound with general composition ABO_, where A and B are both cations namely, A=Sr_+ and B=Ru__. Structural Rietveld refinements of the Sr_YRu___Ir_O6 x-ray powder diffraction data were carried out and the spectra could be indexed according to the monoclinic P2_/n space group. The lattice parameters are found to increase nearly linearly with Ir substitution, consistent with Vegard's law. Field-cooled (FC) magnetic susceptibility measurements on pure Sr_YRuO_ reveal a broad symmetric peak centered near TN _26 K. Previous studies have associated the TN _ 26 K peak with the AFM ordering temperature. Specific heat measurements for pure Sr_YRuO_ show two well-defined peaks, one of which correlates relatively well in temperature with the feature at TN _26 K observed in the FC magnetic susceptibility data. The mechanism driving the second feature in CP (T) at _ 30 K is not well established. The broad peak in magnetic susceptibility along with the two overlapping features in specific heat are suggestive of AFM order and complex, frustrated magnetic behavior. It has been suggested that the feature at _ 30 K may correspond to a slight structural modification or perhaps that it is a result of competing channels for the superexchange interactions, e.g. Ru-O-O-Ru and Ru-O-Y-O-Ru. In order to probe the origin and stability of the magnetically ordered state, the study consisted in measurements of a series of Ir-doped compounds with partial Ir substitution for Ru. Previous studies have verified that Sr-2116 orders magnetically at the Ru__ site. The partial substitution of the less magnetic Ir for Ru drives down the ordering temperature and weakens the AFM state. Measurements of entropy loss in the ordered state and thermal conductivity are discussed. Also addressed are the issues of measurement artifacts, including the effect of the remnant flux in the superconducting magnet, which leads to the observation of a "negative" magnetic susceptibility at low temperatures; time-dependence near the AFM ordering temperature; as well as the possible contribution of radiative heat loss to the T_ behavior in thermal conductivity above _ 125 K. The effects of these measurement artifacts and remedies will be discussed along with the results of the study and plans for further investigation of these exotic materials.