The cold, magnetized plasma in the Earth's magnetosphere supports two ultralow- frequency plasma wave modes. Both these modes may exhibit resonant oscillations in the magnetosphere cavity. Theoretical and numerical studies have predicted the existence of cavity/waveguide resonance modes, yet experimental evidence is sparse. In this paper we detail the expected structure of these modes using both one dimensional (1-D) and three-dimensional (3-D) magnetohydrodynamic (MHD) numerical models. The cavity/waveguide mode structures are examined in order to develop experimental detection methods suitable for spacecraft electric and magnetic field perturbation data. Cavity mode resonances in the 1-D model suggest a detection method based on wave polarization using the radial (bx) and field-aligned (bz) magnetic perturbations. However, when implemented, this method failed to identify cavity/waveguide modes in the magnetic field data recorded by Active Magnetospheric Particle Tracer Explorers/CCE for events that showed pronounced field line resonances in the azimuthal (by) channel. An examination of data from a 3-D MHD numerical simulation showed that the cavity/waveguide resonant signature was identified best in bz component data. Consequently, a wave mode detection method using the bz data from two spatially separated satellites is discussed. Magnetometer data examples from the ISEE 1 and 2 spacecraft show that field line resonances appear in the by data even when the coherence length of the bz data is less than 0.4 RE.