We present a fabrication method to obtain freestanding optical microcavities in Single Crystal Diamond (SCD), based on a combination of Reactive Ion Etching (RIE) and multidirectional Focused Ion Beam (FIB) milling, and we report for the first time experimental optical characterization of freestanding diamond optical microdisk resonators obtained by this fabrication method. Patterning of the optical microcavities is achieved by contact photolithography on single crystal CVD diamond plates (3 mm x 3 mm x 0.15 mm), using a SiO2 hard mask and optimized O2 diamond plasma etching, resulting in multiple circular pillars in a single etch step. Individual pillars are subsequently undercut by multi-directional FIB milling from two orthogonal directions, shaping the anchor to the bulk substrate. Sequential FIB thinning and smoothing of the disks allows obtaining freestanding optical microcavities. During FIB milling, an Al/Cr layer (50 nm/75 nm) is used to ground the diamond substrate, simultaneously limiting ion implantation and reducing FIB induced edge rounding. We experimentally probe the cavities by a tunable laser, coupled to the resonator by a tapered single mode fiber. The spectral response of a typical microdisk (diameter 5.9 μm, thickness 800 nm) in transmission over the tuning range of the laser (1485 nm to 1550 nm) reveals multiple optical resonances with a Free Spectral Range of 52.5 nm and optical Q-factors attaining up to 1500 (at 1496 nm). To our knowledge, this is the first time that freestanding optical microdisk resonators are demonstrated in Single Crystal Diamond by a combination of RIE and multidirectional FIB milling, providing a path for high-Q optical cavities in diamond.