The physics programme of the TOTEMexperiment requires the detection of very forward protons scattered by only a few microradians out of the LHC beams. For this purpose, stacks of planar Silicon detectors have been mounted in moveable near-beam telescopes (Roman Pots) located along the beamline on both sides of the interaction point. In order to maximise the proton acceptance close to the beams, the dead space at the detector edge had to be minimised. During the detector prototyping phase, different sensor technologies and designs have been explored. A reduction of the dead space to less than 50 mu m has been accomplished with two novel silicon detector technologies: one with the Current Terminating Structure (CTS) design and one based on the 3D edge manufacturing. This paper describes performance studies on prototypes of these detectors, carried out in 2004 in a fixed-target muon beam at CERN's SPS accelerator. In particular, the efficiency and accuracy in the vicinity of the beam-facing edges are discussed.