Background: Long-term care facilities (LTCFs) are particularly vulnerable to nosocomial outbreaks of coronavirus disease 2019 (COVID-19), with high rates of transmission and mortality. Timely epidemiological surveillance is essential to detect and respond to outbreaks, but testing resources are highly limited in the current pandemic context. Methods: We used an individual-based transmission model to simulate COVID-19 spread along inter-individual contact networks in the LTCF setting. A range of surveillance strategies were evaluated for their ability to detect simulated outbreaks, assuming limited availability of standard RT-PCR tests. Various epidemiological scenarios were considered, including COVID-19 importation from patient transfers or staff members infected in the community. Findings: We estimated a median delay of 7 (95% uncertainty interval: 2-15) days from importation of an asymptomatic COVID-19-infected patient to first presentation of COVID-19 symptoms among any patients or staff, at which point an additional 7 (0-25) individuals were infected but did not (yet) show symptoms. Across a range of scenarios, the reference surveillance strategy (testing individuals with COVID-like symptoms with signs of severity) took a median 11-21 days to detect an outbreak. Group testing (pooling specimens from multiple individuals for a single RT-PCR test) patients and staff with any COVID-like symptoms was both the most timely and efficient strategy, detecting outbreaks up to twice as quickly as the reference, and more quickly than other considered strategies while using fewer tests. Maximizing use of available tests via testing cascades was more effective than group testing only when substantial testing resources were available (on the order of 1 test/20 beds/day). Including not merely those with symptoms but also newly admitted patients in group tests and testing cascades reduced delays in outbreak detection for LTCFs actively admitting patients potentially already infected with COVID-19. Interpretation: Improving COVID-19 surveillance can alert healthcare institutions to emerging outbreaks before they escalate, informing a need for urgent public health intervention in settings with ongoing nosocomial transmission.