Current waveguide flange standards do not allow for the accurate fitting of microchips, due to the large mechanical tolerances of the flange alignment pins and the brittle nature of Silicon, requiring greatly oversized alignment holes on the chip to fit worst-case fabrication tolerances, resulting in unacceptably large misalignment error for sub-THz frequencies. This paper presents, for the first time, a new method for directly aligning micromachined Silicon chips to standard, i.e. unmodified, waveguide flanges with alignment accuracy significantly better than the waveguide-flange fabrication tolerances, through the combination of a tightly-fitting circular and an elliptical alignment hole on the chip. A Monte Carlo analysis predicts the reduction of the mechanical assembly margin by a factor of 5.5 compared to conventional circular holes, reducing the potential chip misalignment from 46 μm to 8.5 μm for a probability of fitting of 99.5%. For experimental verification, micromachined waveguide chips using either conventional (oversized) circular or the proposed elliptical alignment holes were fabricated and measured. A reduction in the standard deviation of the reflection coefficient by a factor of up to 20 was experimentally observed from a total of 200 measurements with random chip placement, exceeding the expectations from the Monte Carlo analysis. To our knowledge, this paper presents the first solution for highly accurate assembly of micromachined waveguide chips to standard waveguide flanges, requiring no custom flanges or other tailor-made split blocks.