Recent near infrared observations of starburst galaxies and active galactic nuclei have revealed that such objects are often prominent sources of forbidden [Fe II] emission lines at 1.26 and 1.64 microns. The origin of the [Fe II] emission is uncertain and has been attributed to hot gas in HII regions, photon-dominated regions, or supernova remnants associated with star-formation, and to X-ray irradiated or shocked gas associated with non-stellar energy sources in active galactic nuclei. Identification of the primary [Fe II] emission sources is crucial in order to use the Fe II emission lines as quantitative diagnostics of processes in SBGs and AGNs. The ISO SWS offers the opportunity to study such infrared [Fe II] emission sources in a way never attempted before. We propose to use the SWS to observe the mid-infrared 5.34, 17.93, and 25.98 micron lines of [Fe II] in a sample of objects containing Seyfert 1's and 2's, and starburst galaxies. Our measurements will provide new constraints on the physical conditions in the [Fe II] emitting regions, and will provide unique information about the gas temperatures, densities, sizes and iron abundances in them. Our model computations show that these lines should be easily detectable in galaxies which produce bright near infrared [Fe II] emission. Our proposed observations will complement several SWS measurements of Galactic [Fe II] emission sources which will be carried out within the Central Programme. Our ISO observations will provide crucial new information about the nature of infrared extra- galactic [Fe II] emitters.