A robotically articulated inspection scope (56, 69) inserted into a pilot fuel nozzle port (58) of a turbine engine (20) for in-situ measurement of gaps (59) between tips of turbine blades (40A) and the surrounding shroud (44). A non-contact gap measuring device (52) on a distal end (79) of the scope may be navigated through a combustor (28) and transition duct (34) into a position proximate a blade tip gap. The scope may be controlled via computer (68) via a robotic drive (66) affixed to the pilot fuel nozzle port. Multiple scopes may be used to measure gaps (59A-D) at multiple azimuths of the turbine simultaneously. The turbine disk (37) may be rotated on its operating turning gear to sequentially measure each blade at each azimuth. The computer may memorize an interactively navigated path for subsequent automated positioning.