We report the isolation of two human IgG1k monoclonal antibodies (mAbs) directed against the SARS-CoV-2 spike protein. These mAbs were isolated from two donors who had recovered from COVID-19 infection during the first pandemic peak in the Lombardy region of Italy, the first European and initially most affected region in March 2020. We used the method of EBV immortalization of purified memory B cells and supernatant screening with a spike S1/2 assay for mAb isolation. This method allowed rapid isolation of clones, with one donor showing about 7% of clones positive against spike protein, whereas the other donor did not produce positive clones out of 91 tested. RNA was extracted from positive clones 39–47 days post-EBV infection, allowing VH and VL sequencing. The same clones were sequenced again after a further 100 days in culture, showing that no mutation had taken place during in vitro expansion. The B cell clones could be expanded in culture for more than 4 months after EBV immortalization and secreted the antibodies stably during that time, allowing to purify mg quantities of each mAb for functional assays without generating recombinant proteins. Unfortunately, neither mAb had significant neutralizing activity in a virus infection assay with several different SARS-CoV-2 isolates. The antibody sequences are made freely available.