Ligands that have an affinity for protein targets can be screened very effectively by exploiting favorable properties of long-lived states (LLS) in NMR spectroscopy. In this work, we describe the use of LLS for competitive binding experiments to measure accurate dissociation constants of fragments that bind weakly to the ATP binding site of the N-terminal ATPase domain of heat shock protein 90 (Hsp90), a therapeutic target for cancer treatment. The LLS approach allows one to characterize ligands with an exceptionally wide range of affinities, since it can be used for ligand concentrations [L] that are several orders of magnitude smaller than the dissociation constants K-D. This property makes the LLS method particularly attractive for the initial steps of fragment-based drug screening, where small molecular fragments that bind weakly to a target protein must be identified, which is a difficult task for many other biophysical methods.