According to one aspect, a magnetic resonance (NMR or MRI) phantom includes a spherical or quasi-spherical casing enclosing an internal chamber, and an internal phantom structure situated within the internal chamber. The casing includes alignment features allowing the sequential alignment/orientation of the phantom along three orthogonal axes. In some embodiments, the casing is shaped as a quasi-spherical intercyl having an outer surface defined by the intersection of three orthogonal cylinders. In some embodiments, the casing may be shaped as a sphere having orthogonal registration holes or channels sized to accommodate a corresponding protrusion or ridge in a phantom holder; the casing may also include protrusions or ridges sized to fit into a matching hole or channel defined in a holder. One or more internal phantom plates may include air bubble transfer apertures allowing air bubbles to flow between opposite sides of a plate as a liquid-filled phantom is rotated.