Consideration of information from multiple modalities has been shown to have increased diagnostic power in breast imaging. As a result, new techniques such as microwave imaging continue to be developed. Interpreting these novel image modalities is a challenge, requiring comparison to established techniques such as the gold standard X-ray mammography. However, due to the highly deformable nature of breast tissues, comparison of 3D and 2D modalities is a challenge. To enable this comparison, a registration technique was developed to map features from 2D mammograms to locations in the 3D image space. This technique was developed and tested using magnetic resonance (MR) images as a reference 3D modality, as MR breast imaging is an established technique in clinical practice. The algorithm was validated using a numerical phantom then successfully tested on twenty-four image pairs. Dice's coefficient was used to measure the external goodness of fit, resulting in an excellent overall average of 0.94. Internal agreement was evaluated by examining internal features in consultation with a radiologist, and subjective assessment concludes that reasonable alignment was achieved.