Establishing how many people have been infected by SARS-CoV-2 remains an urgent priority for controlling the COVID-19 pandemic. Serological tests that identify past infection can be used to estimate cumulative incidence, but the relative accuracy and robustness of various sampling strategies has been unclear. We developed a flexible framework that integrates uncertainty from test characteristics, sample size, and heterogeneity in seroprevalence across subpopulations to compare estimates from sampling schemes. Using the same framework and making the assumption that seropositivity indicates immune protection, we propagated estimates and uncertainty through dynamical models to assess uncertainty in the epidemiological parameters needed to evaluate public health interventions, and found that sampling schemes informed by demographics and contact networks outperform uniform sampling. The framework can be adapted to optimize serosurvey design given test characteristics and capacity, population demography, sampling strategy, and modeling approach, and can be tailored to support decision-making around introducing or removing interventions.