Buried threats such as Improvised Explosive Devices (IEDs) and UneXploded Ordnance (UXO) can be composed of different materials including metal, carbon fiber, carbon rods, and nonconducting material such as wood, rubber, fuel oil, and plastic. Electromagnetic induction (EMI) instruments have been traditionally used to detect high electric conductivity discrete targets such as metal UXO. The frequencies used for this EMI regime have typically been less than 100 kHz. To detect intermediate conductivity objects like carbon fiber, higher frequencies up to the low megahertz range are required in order to capture characteristic relaxation responses. Nonconducting voids in an otherwise conducting background medium like soil channel currents around the void. These channeling currents exhibit relaxation responses similar to conducting targets but with a much higher frequency response. Nonconducting plastic landmines can be considered a void plus small metallic parts such as the firing pin, and a characteristic relaxation response due to both the void and the metal parts can be obtained which can reduce false alarms from EMI instruments that detect only the metal. To predict EMI phenomena at frequencies up to 15MHz, we modeled the response of conducting and nonconducting targets using the Method of Auxiliary Sources. Our high-frequency electromagnetic induction (HFEMI) instrument is able to acquire EMI data at frequencies up to that same high limit. Modeled and measured characteristic relaxation signatures compare favorably and indicate new sensing possibilities in a variety of scenarios including the detection of voids and landmines.