Background During the COVID-19 pandemic, swab tests proved to be effective in containing the infection and served as a means for early diagnosis and contact tracing. However, little evidence exists regarding the correct timing for the execution of the swab test, especially for asymptomatic individuals and health care workers. Objective The objective of this study was to analyze changes in the positive findings over time in individual SARS-CoV-2 swab tests during a health surveillance program. Methods The study was conducted with 2071 health care workers at the University Hospital of Verona, with a known date of close contact with a patient with COVID-19, between February 29 and April 17, 2020. The health care workers underwent a health surveillance program with repeated swab tests to track their virological status. A generalized additive mixed model was used to investigate how the probability of a positive test result changes over time since the last known date of close contact, in an overall sample of individuals who tested positive for COVID-19 and in a subset of individuals with an initial negative swab test finding before being proven positive, to assess different surveillance time intervals. Results Among the 2071 health care workers in this study, 191 (9.2%) tested positive for COVID-19, and 103 (54%) were asymptomatic with no differences based on sex or age. Among 49 (25.7%) cases, the initial swab test yielded negative findings after close contact with a patient with COVID-19. Sex, age, symptoms, and the time of sampling were not different between individuals with an initial negative swab test finding and those who initially tested positive after close contact. In the overall sample, the estimated probability of testing positive was 0.74 on day 1 after close contact, which increased to 0.77 between days 5 and 8. In the 3 different scenarios for scheduled repeated testing intervals (3, 5, and 7 days) in the subgroup of individuals with an initially negative swab test finding, the probability peaked on the sixth, ninth and tenth, and 13th and 14th days, respectively. Conclusions Swab tests can initially yield false-negative outcomes. The probability of testing positive increases from day 1, peaking between days 5 and 8 after close contact with a patient with COVID-19. Early testing, especially in this final time window, is recommended together with a health surveillance program scheduled in close intervals.