Examined and interpreted are the transmission characteristics of the azimuthally magnetized ferrite-loaded coaxial waveguide - a canonical structure for digital remanent phaser designs, using the versatile and flexible Method of Lines. Emphasis is placed on TE01 mode exhibiting anisotrophic effects of phase shifting and magnetically controlled cutoff dependent on the direction of remanent magnetization. A rigorous numerical analysis of field distribution over the guide cross-section, the eigenvalue spectrum and transmission characteristics is performed, giving a great deal of insight and essential quantitative information on propagation phenomena in the gyrotrophic structure.