A filter designed with the mode-matching method does usually not require manual tuning when manufactured. In order to accomplish this the dimensional uncertainties - introduced by the manufacturing process - must be carefully controlled.

The essence of the mode-matching method is that the structure to be analyzed is sub divided into cylindrical slices (for a metal insert filter these slices would consist of empty- and bifurcated waveguide sections). The modes which can propagate in each section, including evanescent modes, are set up and the complex amplitudes of the modes are matched across the boundary of the slice to the next slice, bearing in mind the boundary conditions. 

In order to solve for the complex amplitudes, it is necessary to evaluate eigen-modes of rectangular cross-sections. Electric and magnetic field components within each region are expressed in terms of sine functions. 
By matching tangential fields at the interfaces, a set of linear equations can be derived. Both the propagation coefficients and field distributions of eigen modes can then be obtained by solving the simultaneous equations. The modes can either be transverse electric/magnetic or hybrid depending on the presence of dielectrics. 

Once the modal distributions are known coupling integrals between a pair of modes, one each from either sides, are evaluated at a junction between two cylindrical sections. The resulting complex coupling coefficients are cast into a matrix form and by performing algebraic matrix operations the multi-mode scattering matrix of the junction can be obtained. 
The overall scattering matrix of the structure can subsequently be obtained by cascading the scattering matrices. The desired complex amplitudes at the output of the structure are then obtained by multiplying the overall scattering matrix with the input excitation coefficients.

F. Arndt et al. "Modal S-matrix method for the optimum design of inductively direct-coupled cavity filters" IEE Proceedings, vol. 133, Pt.H, No 5, Oct. 1986

J. Bornemann et al. "Optimized low-insertion-loss millimetre-wave fin-line and metal insert filters"  The Radio and Electronic Engineer, vol. 52, No 11/12, pp. 513-521, Nov./Dec. 1982

F.E. Gardiol  "Higher-Order Modes in Dielectrically Loaded Rectangular Waveguides"  IEEE Trans. Microwave Theory Tech., vol. MTT-16, No. 11 pp.919-924, Nov. 1968