The intermetallic magnesium compounds CeCuMg and GdCuMg as well as the ternary Laves phases RECu4Mg (RE=Sm, Gd–Tm) were synthesized from the elements by different annealing sequences in high-frequency and muffle furnaces using niobium ampoules as crucibles. All samples were characterized through the lattice parameters using X-ray powder diffraction (Guinier technique). Two structures were refined from single-crystal X-ray diffractometer data: a=764.75(6), c=414.25(4) pm, space group P6̅2m, wR2=0.0389, 338 F2 values, 15 parameters for CeCuMg (ZrNiAl type) and a=723.18(2) pm, space group F4̅3m, wR2=0.0818, 91 F2 values, eight parameters for Gd1.06(3)Cu4Mg0.94(3) (MgCu4Sn type). The Laves phase shows a small homogeneity range (Gd/Mg mixing). An investigation of the magnetocaloric effect (MCE) of ferromagnetic GdCuMg (ZrNiAl type; TC=82 K) revealed a magnetic entropy change of ΔSM=6.5 J kg−1 K−1 and a relative cooling power of RCP=260 J kg−1 for a field change from 0 to 70 kOe, classifying GdCuMg as a moderate magnetocaloric material for the T=80 K region. Of the Laves phases RECu4Mg, SmCu4Mg shows van-Vleck paramagnetism above a Néel temperature of 10.8(5) K, whereas GdCu4Mg and TbCu4Mg undergo antiferromagnetic phase transitions at about 48 and 30 K, respectively. TmCu4Mg shows Curie-Weiss behavior in the entire temperature range. The electrical resistivity of SmCu4Mg and the specific heat capacity of GdCu4Mg were measured for further characterization.