Low drop-out (LDO) regulator circuits and methods that can operate at high frequencies without the adverse consequences of an oscillatory resonance effect from a capacitive load. In a first embodiment, a low pass filter (LPF) is coupled to the LDO and tuned to cancel the oscillatory resonance effect. In a second embodiment, the LPF is a second-order LPF and/or programmable. Since the tuning values of the programmable LPF may be programmatically selected, a much greater range of external capacitors values (with attendant ESR and ESL values), as well as a wider range of system parasitic capacitances, can be accommodated while maintaining system stability. Some variants of the second embodiment include an oscillation detector and filter bit control circuit that allows the tuning values of the programmable LPF to be dynamically determined and re-determined. An impedance-lowering device may be coupled to lower the impedance of the connection to the LPF.