The recent outbreak of SARS-CoV-2 (2019-nCoV) virus has highlighted the need for fast and efficacious vaccine development. Stimulation of a proper immune response that leads to protection is highly dependent on presentation of epitopes to circulating T-cells via the HLA complex. SARS-CoV-2 is a large RNA virus and testing of all of its overlapping peptides in vitro to deconvolute an immune response is not feasible. Therefore, HLA-binding prediction tools are often used to narrow down the number of peptides to test. We tested 19 epitope-HLA-binding prediction tools, and using an in vitro peptide-MHC stability assay, we assessed 777 peptides that were predicted to be good binders across 11 MHC alleles. In this investigation of potential SARS-CoV-2 epitopes, we found that current prediction tools vary in performance when assessing binding stability, and they are highly dependent on the MHC allele in question. Designing a COVID-19 vaccine where only a few epitope targets are included is therefore a very challenging task. Here, we present 174 SARS-CoV-2 epitopes with high prediction binding scores, validated to bind stably to 11 HLA alleles. Our findings may contribute to the design of an efficacious vaccine against COVID-19.