Ethylene vinyl alcohol copolymer (EVOH) is a key material of interest as a functional barrier against substances migrating from recycled paperboard, due to its outstanding barrier properties. Three multilayer films containing two different grades of EVOH, L171B (3 µm) and F171B (3 and 5 µm), were benchmarked against a multilayer film containing polyamide 6/6.6 copolymer (PA 6/6.6, 3 µm) and monolayer polyethylene terephthalate (PET, 12 µm). The 5 films were evaluated as barrier materials against 5 surrogate substances simulating different migrants potentially present in recycled paperboard: n-heptadecane (C17) as a mineral oil-saturated hydrocarbon (MOSH), 4-methylbenzophenone (MBP) as a photoinitiator, di-n-propyl phthalate (DPP) as a plasticiser, and anthracene (ANT) and perylene (PER) as mineral oil aromatic hydrocarbons (MOAHs). The test was accelerated at 60°C for 25 days, which is equivalent to a shelf life of 2 years at 25°C. All films containing 3 or 5 µm EVOH were found to be good barriers, showing no breakthrough values over 1% of the initial concentration found in the paperboard, and they could easily compete with 12 µm PET. The multilayer with 3 µm PA 6/6.6 showed higher breakthrough values for both MBP and DPP than the other materials although still below the 1% threshold value. However, ANT showed substantial breakthrough values of nearly 2%, indicating that PA 6/6.6 might not offer enough protection against low-weight MOAH components.