We present measurements of the basic properties of Ce(2)Ge(2)Mg, Yb(2)Pt(2)Pb and Ce(2)Pt(2)Pb, which are members of a new class of geometrically frustrated magnets R(2)T(2)X (R = rare earth, T = transition metal, X = main group). Here, the moment-bearing R atoms are confined to layers where they are arranged in the Shastry-Sutherland lattice. Magnetic susceptibility and specific heat measurements indicate that Ce(2)Ge(2)Mg orders antiferromagnetically at 9.4 K and Yb(2)Pt(2)Pb at 2.07 K. No long ranged order is observed in Ce(2)Pt(2)Pb above 0.05 K. Analysis of Schottky peaks in the specific heat indicates that all three compounds have doublet ground states that are well separated in energy from the excited states of the crystal-field-split manifold. Electrical resistivity measurements show that Ce(2)Ge(2)Mg and Yb(2)Pt(2)Pb are excellent metals with small residual resistivities. However, the measured resistivity of Ce(2)Pt(2)Pb is large and almost temperature-independent, suggesting that strong disorder or perhaps strong quantum critical fluctuations saturate the quasiparticle scattering in this compound. The magnetic entropy develops very slowly above the onset of antiferromagnetic order and we discuss the possibility that a nonordered fluid of dimerized moments exists above T(N) in Ce(2)Ge(2)Mg and Yb(2)Pt(2)Pb, and for a wide range of temperatures in Ce(2)Pt(2)Pb, which appears to be close to a frustration-driven quantum critical point.