No-Carrier-Added186Re was produced using the186W(p,n)186Re nuclear reaction with 13.6 MeV protons on thick targets of 99.79% isotopically enriched186WO3. The theoretical excitation functions for producing186Re, and possible radionuclidic impurities of182Re,183Re, and184Re were calculated using the ALICE code. Cross-sections of the186W(p,n)186Re reaction were measured up to 20 MeV using the stacked target method with thin foils of natural composition tungsten metal. The experimental and theoretical excitation functions were in good agreement. Targetry used at the TIARA cyclotron, and a radiochemical separation scheme for186Re are described.