Two B-site ordered double perovskites, La2LiMoO6 and Ba2YMoO6, based on the S= 12 ion, Mo5+, have been investigated in the context of geometric magnetic frustration. Powder neutron diffraction, heat capacity, susceptibility, muon-spin relaxation (μSR), and Y 89 NMR-including magic-angle spinning (MAS) NMR data have been collected. La2LiMoO6 crystallizes in P21/n with a=5.59392(19) Å, b=5.69241(16) Å, c=7.88029(22) Å, and β=90.2601(30)° at 299.7 K, while Ba2YMoO6 is cubic, Fm3m, with a=8.39199(65) Å at 297.8 K. Ba2YMoO6 shows no distortion from cubic symmetry even at 2.8 K in apparent violation of the Jahn-Teller theorem for a t2g1 ion. Y 89 NMR MAS data indicate about a 3% level of Y/Mo site mixing. La2LiMoO6 deviates strongly from simple Curie-Weiss (C-W) paramagnetic behavior below 150 K and zero-field-cooled/field-cooled (ZFC/FC) irreversibility occurs below 20 K with a weak, broad susceptibility maximum near 5 K in the ZFC data. A Curie-Weiss fit shows a reduced μeff=1.42μB, (spin only=1.73μB) and a Weiss temperature, θC, which depends strongly on the temperature range of the fit. Powder neutron diffraction and heat capacity show no evidence for long-range magnetic order to 2 K. On the other hand oscillations develop below 20 K in μSR indicating at least short-range magnetic correlations. Susceptibility data for Ba2YMoO6 also deviate strongly from the C-W law below 150 K with a nearly spin only μeff=1.72μB and θC=−219(1) K. There is no discernible ZFC/FC irreversibility to 2 K. Heat capacity, neutron powder diffraction, and μSR data show no evidence for long-range order to 2 K but a very broad, weak maximum appears in the heat capacity. The Y 89 NMR paramagnetic Knight shift shows a remarkable local spin susceptibility behavior below about 70 K with two components from roughly equal sample volumes, one indicating a singlet state and the other a strongly fluctuating paramagnetic state. Further evidence for a singlet state comes from the behavior of the relaxation rate, 1/T1. These results are discussed and compared with those from other isostructural S= 12 materials and those based on S=3/2 and S=1.