Microwave tomography (MWT) differs from the current forms of biomedical imaging modalities by measuring the dielectric properties in different tissues in order to create an image of the object under evaluation. This technology could be harnessed for the evaluation of a stroke because the areas of the brain that are not being provided oxygen will have a reduced concentration of blood, leading to a reduced relative permittivity (also referred to as dielectric constant). Strokes themselves require accurate diagnosis for proper treatment to be administered. Microwave tomography offers advantages of stroke diagnosis over imaging methods such as magnetic resonance imaging (MRI) and computerized tomography (CT). Like MRIs, microwave tomography passes only non-ionizing radiation through the patient, allowing for multiple safe scans. Because MWT requires only an array of antennas sending a non-ionizing electromagnetic field, which is on the level of the fields sent in cell phones, a patient undergoing a stroke could be diagnosed inside an ambulance with multiple MWT scans, greatly reducing the time before treatment. The challenge for this thesis is to correctly solve an ill-posed problem presented in a microwave tomography system and output an image of the object's electrical properties. The system itself is an inverse problem because the object to be imaged and its properties are unknown. Rather, the incident field and resulting scattered field due to interaction with the object of interest are known. To achieve a unique solution for this problem, a software implementation of a common microwave inversion method known as Born's Iterative Method is realized through MATLAB.