Tuned pick-up coils with high quality factors $Q$ are used in NMR and MRI for high-sensitivity and low-noise detection. However, large $Q$-factors introduce bandwidth issues at low frequency and the associated enhanced currents may cause significant radiation damping effects, especially with hyperpolarised samples. Signal feedback can be used to actively control these currents and adjust the detection bandwidth without resistive losses. Capacitive and inductive coupling methods are compared using detailed models and the operating conditions for efficient feedback with negligible noise penalty are discussed. Several high-impedance commercial preamplifiers have been found to affect the resonance characteristics of tuned coils in a gain-dependent way, or could not be used in low-frequency NMR because of oscillations at large positive gain. This is attributed to an undocumented internal feedback, and could be neutralised using external feedback. The implementation of an inductive coupling scheme to feed a suitably amplified phase-adjusted signal back into the PU coils of low-field NMR systems is described, and three experimental applications are reported. One system is used for NMR studies of distant dipolar field effects in highly polarized liquid $^3$He without or with radiation damping. The moderate intrinsic $Q$-factor ($\approx$7) could be reduced (down to 1) or increased (up to 100) to control transient maser oscillations. Another system was used for MRI of water samples around 2~mT with $Q\approx$190 Litz-wire detection coils. The detection bandwidth was increased by actively reducing the $Q$-factor to obtain uniform sensitivities in images and avoid artifacts introduced by intensity corrections. Finally, parallel acquisition in MRI was performed using two separately tuned detection coils placed above and below the sample. They were actively decoupled using two feedback systems. For an imaging field of view smaller than the sample, artifact-free unfolded images demonstrate the efficiency of this active coil decoupling scheme.