If supersymmetry near the TeV scale is realized in Nature, the pair production of scalar top squarks is expected to be observable at the Large Hadron Collider. Recently, effective field-theory methods were employed to obtain approximate predictions for the cross section for this process, which include soft-gluon emission effects up to nextto- next-to-leading order (NNLO) in perturbation theory. In this work we employ the same techniques to resum soft-gluon emission effects to all orders in perturbation theory and with next-to-next-to-logarithmic (NNLL) accuracy. We analyze the effects of NNLL resummation on the stop-pair production cross section by obtaining NLO+NNLL predictions in pair invariant mass and one-particle inclusive kinematics. We compare the results of these calculations to the approximate NNLO predictions for the cross sections.