Multiport magnetoinductive (MI) devices with directional filter properties are presented. Design equations are developed and solved using wave analysis and dispersion theory, and it is shown that high-performance directional filters can be realised for use both in MI systems with complex, frequency-dependent impedance and in conventional systems with real impedance. Wave analysis is used to reduce the complexity of circuit equations. High-performance MI structures combining directional and infinite rejection filtering are demonstrated, as well as multiple-passband high-rejection filtering. A new method for improving filtering performance through multipath loss compensation is described. Methods for constructing tuneable devices using toroidal ferrite-cored transformers are proposed and demonstrated, and experimental results for tuneable MI directional filters are shown to agree with theoretical models. Limitations are explored, and power handling sufficient for HF RFID applications is demonstrated, despite the use of ferrite materials.