Combustion (or thermoacoustic) instabilities are generated by the interaction between acoustic waves and unsteady combustion. They result in damaging self-excited oscillations. Suppression of combustion instabilities can be achieved using passive control, typically in the form of acoustic dampers. The main drawback of such devices is that they are effective only over a narrow frequency range, and are unable to respond to changes in instability frequency. The focus of this paper is tuned passive control: this involves using a dynamic measurement from the combustor, and varying some feature(s) of the passive damper (i. e. "tuning"it) in response to the measurement. A major advantage is that instabilities of different frequencies can be damped, while actuation is only needed on the time scale over which changes in operating conditions occur (which is much slower than the timescale of the oscillations themselves), making the actuator requirements quite modest. We consider tuned passive control implemented firstly by varying the geometry of a Helmholtz resonator, and secondly by varying two features (a length scale and the bias flow rate) of a perforated liner. Two real-time algorithms are developed; one which tracks the instability frequency/amplitude and another which uses this information to successively tune the passive damper so that its performance is optimised. We demonstrate experimentally that suppression of combustion instabilities is achievable for large changes in instability frequency, where a fixed passive damper would not suffice.