A powerful method of investigating proton-unbound nuclear states by tracking their decay products in flight is discussed in detail. To verify the method, four known levels in F-15, Ne-16, and Na-19 were investigated by measuring the angular correlations between protons and the respective heavy-ion fragments stemming from the precursor decays in flight. The parent nuclei of interest were produced in nuclear reactions of one-neutron removal from Ne-17 and Mg-20 projectiles at energies of 410-450 A MeV. The trajectories of the respective decay products, O-14 + p + p and Ne-18 + p + p, were measured by applying a tracking technique with microstrip detectors. These data were used to reconstruct the angular correlations of the fragments, which provided information on energies and widths of the parent states. In addition for reproducing properties of known states, evidence for hitherto unknown excited states in F-15 and Ne-16 was found. This tracking technique has an advantage in studies of exotic nuclei beyond the proton drip line measuring the resonance energies and widths with a high precision although by using low-intensity beams and very thick targets.