A radiation detection system consisting of two cerium doped lanthanum bromide (LaBr₃:Ce) scintillation detectors in a gamma-gamma coincidence configuration has been used to demonstrate the advantages that coincident detection provides relative to a single detector, and the advantages that LaBr₃:Ce detectors provide relative to high-purity germanium (HPGe) detectors. Measurements have been made in both single and coincident detector configurations with both detector technologies to quantify the performance of each detector configuration permutation. Timing performance and optimization of single and coincident systems have been performed for both detector types. The efficiency and energy resolution of LaBr₃:Ce detectors have been determined and compared to both HPGe detectors and MCNP simulations. Further MCNP simulations have validated single LaBr₃:Ce detector response to a collection of radionuclides. Coincident gamma-ray pairs from the radionuclides ¹⁵²Eu and ¹³³Ba have been identified in a sample that is dominated by ¹³⁷Cs. Gamma-gamma coincidence successfully reduced the Compton continuum from the large ¹³⁷Cs peak, revealed several coincident gamma energies characteristic of these nuclides, and improved the signal-to-noise ratio relative to single detector measurements. LaBr₃:Ce detectors performed at count rates multiple times higher than can be achieved with HPGe detectors. The standard background spectrum consisting of peaks associated with gamma-ray transitions within the LaBr₃:Ce crystal has also been significantly reduced. It is shown that LaBr₃:Ce detectors have the unique capability to perform gamma-gamma coincidence measurements in very high count rate scenarios, which can potentially benefit nuclear safeguards in situ measurements of spent nuclear fuel. As a scoping study for applications to spent nuclear fuel, a series of coincident measurements were made over the course of a month of fission products in irradiated uranium samples of varying enrichment levels.