At the end of 2019, a new disease caused by the novel coronavirus SARS-CoV-2 appeared in Wuhan Province in China. Children seemed to be infected less frequently than adults, and family clusters seemed to play an important role in the spread of the pandemic. The aim of this study is to evaluate the serological profile of children and young adults between 4 and 16 years of age in order to assess the transmission patterns of COVID-19 between cohabitants. The subjects lived with at least one cohabitant who tested positive for the disease using a nasopharyngeal swab. To avoid contact with the disease, families were interviewed by telephone. Forty-nine children and adolescents with a mean age of 11 years were then subjected to a rapid lateral flow chromatographic test. Of them, seven (14.3%) were immunoglobulin G (IgG)-positive, and four (8.2%) were immunoglobulin M (IgM)-positive. In total, 16.3% of the tested sample had antibodies against SARS-CoV-2: this may confirm the lower vulnerability of children to COVID-19, despite the small sample size. The time from the negativization of the cohabitant until the test day may have influenced the results, especially when this timeframe is wide.