  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.
