The propensity of liquid explosives to undergo thermal decomposition via oscillatory rather than classical ignition is exploited as the basis of a new method for detecting explosives: thermal oscillatory microcalorimetry. Computational simulations using a continuous stirred tank reactor model for the explosives triacetone triperoxide and trinitrotoluene are reported. Simulated thermograms for each substance are shown, where the fact that the solid cell heat capacity affects the onset temperature of oscillatory but not classical ignition is used to confirm the capability of an oscillatory signal. Time series in the mild oscillatory regime were Fourier-transformed to give frequency power spectra. For pure triacetone triperoxide in solution the fundamental frequency is $3.82 × 10-4 Hz and for trinitrotoluene in solution the fundamental frequency is 3.46 × 10-3 Hz, under the simulated process conditions. Data were also obtained for a mixture of the substances. The two-parameter bifurcation diagrams of the Hopf bifurcation loci for the pure substances and the mixtures show that for both substances the presence of the other substance shifts the onset of oscillatory behavior to significantly lower temperatures. It is concluded that thermal oscillatory microcalorimetry has potential to be developed as a method for explosives detection that complements existing methods, and may be particularly useful for peroxide explosives, which give no response to the usual nitrogenous explosive detectors. The advantage of the method is intrinsic: harmless liquids will always fail to give an oscillatory signal.