Protons of energies up to about 10(20) eV can be subject to significan
t deflection and energy-dependent time delay in large-scale extragalac
tic or halo magnetic fields of strengths comparable to current upper l
imits. By performing three-dimensional Monte Carlo simulations of nucl
eon propagation, we show how observations of arrival direction and tim
e distributions can be used to measure the structure and strength of l
arge-scale magnetic fields and constrain the nature of the source of u
ltra-high-energy cosmic rays.