In this work, we have studied two novel techniques to enhance the performance of existing geometry-based magnetoresistive RAM physically unclonable function (MRAM PUF). Geometry-based MRAM PUFs rely only on geometric variations in MRAM cells that generate preferred ground state in cells and form the basis of digital signature generation. Here we study two novel ways to improve the performance of the geometry-based PUF signature. First, we study how the choice between specific geometries can enhance the reliability of the digital signature. Using fabrications and simulations, we study how the rectangular shape in the PUF cells is more susceptible to lithography-based geometric variations than the elliptical shape of the same aspect ratio. The choice of rectangular over elliptical masks in the lithography process can therefore improve the reliability of the digital signature from PUF. Second, we present a MRAM PUF architecture and study how resistances in MRAM cells can be used to generate analog voltage output that are easier to detect if probed by an adversary. In the new PUF architecture, we have the choice between selection of rows and columns to generate unique and hard-to-predict analog voltage outputs. For a 64-bit response, the analog voltage output can range between 20 and 500 mV, making it tough for an adversary to guess over this wide range of voltages. This work ends with a discussion on the threat resilience ability of the new improved MRAM PUF to attacks from probing-, tampering-, reuse-, and simulation-based models.