We present predictions for the total cross sections for pair production of squarks and gluinos at the LHC including a combined NNLL resummation of soft and Coulomb gluon effects. We derive all terms in the NNLO cross section that are enhanced near the production threshold, which include contributions from spin-dependent potentials and so-called annihilation corrections. The NNLL corrections at \(\sqrt{s}=13\) TeV range from up to \(20\%\) for squark-squark production to \(90\%\) for gluino pair production relative to the NLO results and reduce the theoretical uncertainties of the perturbative calculation to the \(10\%\) level. Grid files with our numerical results are publicly available.