Nuclear Magnetic Resonance Microscopy (NMRM) images were obtained of a cell of sintered silica (with original grain diameters of 250 to 500 μm) that was initially flooded with water and subsequently with both water and oil. The first acquisition was non-selective and revealed the combined spatial distribution of the water and oil phases. Two subsequent acquisitions, at identical locations, imaged the water and oil phases separately. Each acquisition comprises 16 images with a matrix of 256 by 256 pixels in a square Field of View, FOV, of 1.15 cm, and each image refers to a slice thickness of 100 microns. Volume rendering techniques applied to the image data enable the visualization of the 3D connectivity of the fluid phases in the porous medium. Stereology provides the means by which numerical descriptions of properties of these phases can be efficiently obtained free from model based assumptions, and with known precision. Accordingly, estimates were obtained of the porosity, surface area per unit volume, number per unit volume and mean volume of the ‘regions’ of water and oil within the cell. The overall porosity is estimated as 36.1% (Coefficient of Error, CE, = 3.6%) with oil and water present in the ratio 1.00 to 1.15. At the resolution of the experiment, the water surface measures approximately 2.5 times greater than the oil surface within the cell. There are seven times more ‘regions’ of water than oil with respective mean volumes of 0.03 mm3(Coefficient of Variation, CV, = 19%) and 0.20 mm3(CV = 64%).