The equilibrium geometries, binding energies, and harmonic frequencies of Mg3 and Mg4 have been determined using large atomic natural orbital basis sets in conjunction with high levels of electron correlation. The correlation treatments comprise multireference configuration interaction (MRCI), singles and doubles coupled-cluster (CCSD) theory and the CCSD(T) extension that includes a perturbational estimate of connected triple excitations. As with our previous studies of small Be clusters, the CCSD(T) method is found to reproduce the MRCI results with a remarkable degree of accuracy and at a fraction of the computational cost. Using the CCSD(T) method, full quartic force fields for Mg3 and Mg4 have been determined and anharmonic analyses have been performed using second-order perturbation theory. Vibration-rotation interaction constants and centrifugal distortion constants have also been determined. The fundamental vibrational frequencies are predicted to occur at ν1 (a1′) = 96 and ν2 (e′) = 104 cm-1 for Mg3, and ν1 (a1) = 184, ν2 (e) = 143, and ν3 (t2) = 167 cm-1 for Mg4. Infrared (IR) intensities, evaluated for the IR active modes via the double harmonic approximation, are 0.2 and 2.4 km/mol for the e′ (Mg3) and t2 (Mg4) modes, respectively.