The use of enzymes in preparative biocatalysis often requires tailoring enzyme selectivity by protein engineering. Herein we explore the use of computational library design and molecular dynamics simulations to create variants of limonene epoxide hydrolase that produce enantiomeric diols from meso-epoxides. Three substrates of different sizes were targeted: cis-2,3-butene oxide, cyclopentene oxide, and cis-stilbene oxide. Most of the 28 designs tested were active and showed the predicted enantioselectivity. Excellent enantioselectivities were obtained for the bulky substrate cis-stilbene oxide, and enantiocomplementary mutants produced (S,S)- and (R,R)-stilbene diol with >97 % enantiomeric excess. An (R,R)-selective mutant was used to prepare (R,R)-stilbene diol with high enantiopurity (98 % conversion into diol, >99 % ee). Some variants displayed higher catalytic rates (kcat) than the original enzyme, but in most cases KM values increased as well. The results demonstrate the feasibility of computational design and screening to engineer enantioselective epoxide hydrolase variants with very limited laboratory screening.