India's lockdown and subsequent restrictions against SARS-CoV-2, if lifted without any other mitigations in place, could risk a second wave of infection. A test-and-isolate strategy, using PCR diagnostic tests, could help to minimise the impact of this second wave. Meanwhile, population-level serological surveillance can provide valuable insights into the level of immunity in the population. Using a mathematical model, consistent with an Indian megacity, we examined how seroprevalence data could guide a test-and-isolate strategy, for fully lifting restrictions. For example, if seroprevalence is 20% of the population, we show that a testing strategy needs to identify symptomatic cases within 5-8 days of symptom onset, in order to prevent a resurgent wave from overwhelming hospital capacity in the city. This estimate is robust to uncertainty in the effectiveness of the lockdown, as well as in immune protection against reinfection. To set these results in their economic context, we estimate that the weekly cost of such a PCR-based testing programme would be less than 2.1% of the weekly economic loss due to the lockdown. Our results illustrate how PCR-based testing and serological surveillance can be combined to design evidence-based policies, for lifting lockdowns in Indian cities and elsewhere.