SIMPLE is a superheated droplet detector (SDD) experiment designed to search for the evidence of spin-dependent weakly interacting neutralino dark matter (WIMPs). SDDs, a type of emulsion detector, consist of a uniform suspension of superheated liquid droplets in a compliant material such as a polymeric or aqueous gel. We report on the first neutron spectrometry experiments with SIMPLE SDDs, a spin-off of the neutron detector calibrations performed at the Portuguese Research Reactor. SIMPLE SDDs differ from most SDDs available commercially as they have a 10 times higher loading factor, containing 103 times more freon than their commercial counterparts and a 100 times larger volume. We have analysed the response of SIMPLE SDDs to two quasi-monochromatic neutron beams of energies 54 and 144 keV obtained with passive filters. Results show that the characteristic peaks in the fluence distribution of both filters could be determined and their energy position obtained using a simple thermodynamic relation.