Blood products are essential components of any healthcare system, and their safety, in terms of being free of transfusion-transmittable infections, is crucial. While the Food and Drug Administration (FDA) in the United States requires all blood donations to be tested for a set of infections, it does not dictate which particular tests should be used by blood collection centers. Multiple FDA-licensed blood screening tests are available for each infection, but all screening tests are imperfectly reliable and have different costs. In addition, infection prevalence rates and several donor characteristics are uncertain, while surveillance methods are highly resource- and time-intensive. Therefore, only limited information is available to budget-constrained blood collection centers that need to devise a post-donation blood screening scheme so as to minimize the risk of an infectious donation being released into the blood supply. Our focus is on "robust" screening schemes under limited information. Toward this goal, we consider various objectives, and characterize structural properties of the optimal solutions under each objective. This allows us to gain insight and to develop efficient algorithms. Our research shows that using the proposed optimization-based approaches provides robust solutions with significantly lower expected infection risk compared to other testing schemes that satisfy the FDA requirements. Our findings have important public policy implications.