We present state-of-the-art cross section predictions for the production of supersymmetric squarks and gluinos at the upcoming LHC run with a centre-of-mass energy of $sqrt{s} = 13$ and $14$ TeV, and at potential future $pp$ colliders operating at $sqrt{s} = 33$ and $100$ TeV. The results are based on calculations which include the resummation of soft-gluon emission at next-to-leading logarithmic accuracy, matched to next-to-leading order supersymmetric QCD corrections. Furthermore, we provide an estimate of the theoretical uncertainty due to the variation of the renormalisation and factorisation scales and the parton distribution functions.