The level of experimental precision that will be achieved with LHC Run-III data and in the forthcoming High Luminosity stage calls for equally accurate theoretical predictions to compare with. Here we present updated cross section calculations for the electroweak production of SUSY particles at the LHC with aNNLO+NNLL (approximate next-to-next-to-leading-order plus next-to-next-to-leading-logarithmic) accuracy. Results are shown for slepton pair production and for electroweakinos pair production in their mostly higgsino or gaugino configuration, finding a further significant reduction of the factorisation and renormalisation scale dependence that stabilises the predictions to the permil level.