A class of frequency-reconfigurable input-reflectionless/absorptive RF/microwave filters is presented. They consist of tunable complementary-duplexer architectures that are composed of a main and an auxiliary channel with opposite filtering transfer functions. By loading the auxiliary channel with a reference-impedance resistor and by taking the output node of the main channel as the output terminal of the overall circuit, a filtering network of the same type of the main channel with theoretically perfect input-reflectionless behavior at all frequencies can be realized. This technique can be applied to design spectrally agile completely input-reflectionless filters with any kind of transfer function, such as low-pass, high-pass, and single/multiband bandpass/bandstop filters. The theoretical analysis of the first-order absorptive bandpass/bandstop filtering sections based on a coupling-matrix formulation is detailed. Furthermore, the synthesis of high-selectivity reflectionless filters either by cascading multiple first-order cells or using high-order channels in a single complementary duplexer is also described. For practical-demonstration purposes, frequency-tunable lumped-element and microstrip prototypes are manufactured and characterized. They correspond to first- and second-order bandpass/bandstop filters. In addition, their in-series cascade connection is used to implement a bandpass filter with spectrally controllable passband and out-of-band notches.