A downhole measurement tool includes at least one non-planar antenna configured for transmitting and/or receiving electromagnetic radiation. The non-planar antenna includes at least one non-planar loop of antenna wire deployed about a tool body. In one exemplary embodiment, the non-planar antenna may be thought of as being bi-planar in that it includes first and second sections defining first and second intercepting geometric planes. In another exemplary embodiment, the axial separation between the non-planar loop of antenna wire and a circular centerline of the antenna varies substantially sinusoidally with respect to an azimuth angle about the circumference of the tool. Exemplary non-planar antennae in accordance with the invention may be advantageously configured to transceive substantially pure x-, y-, and z-mode radiation.