Although COVID-19 vaccines are globally available, waning immunity and emerging vaccine-evasive variants of concern have hindered the international response and transition to a post-pandemic era. Testing to identify and isolate infectious individuals remains the most proactive strategy for containing an ongoing COVID-19 outbreak. We developed a stochastic, compartmentalized model to simulate the impact of using Reverse Transcriptase Polymerase Chain Reaction (RT-PCR) assays, rapid antigen tests, and vaccinations on SARS-CoV-2 spread. We compare testing strategies across an example high-income country (the United States) and low- and middle-income country (India). We detail the optimal testing frequency and coverage in the US and India to mitigate an emerging outbreak even in a vaccinated population: overall, maximizing testing frequency is most important, but having high testing coverage remains necessary when there is sustained transmission. A resource-limited vaccination strategy still requires high-frequency testing to minimize subsequent outbreaks and is 16.50% more effective in reducing cases in India than the United States. Tailoring testing strategies to transmission settings can help effectively reduce disease burden more than if a uniform approach were employed without regard to epidemiological variability across locations.