De novo membrane protein structure prediction is limited to small proteins due to the conformational search space quickly expanding with length. Long-range contacts (24+ amino acid separation)-residue positions distant in sequence, but in close proximity in the structure, are arguably the most effective way to restrict this conformational space. Inverse methods for co-evolutionary analysis predict a global set of position-pair couplings that best explain the observed amino acid co-occurrences, thus distinguishing between evolutionarily explained co-variances and these arising from spurious transitive effects. Here, we show that applying machine learning approaches and custom descriptors improves evolutionary contact prediction accuracy, resulting in improvement of average precision by 6 percentage points for the top 1L non-local contacts. Further, we demonstrate that predicted contacts improve protein folding with BCL::Fold. The mean RMSD100 metric for the top 10 models folded was reduced by an average of 2 Å for a benchmark of 25 membrane proteins.