The studied heavy fermion Ce3Pd20Si6 (CPS) and the quantum magnetic m-PhNO2BNO (BoNO) systems feature a rich phase diagram at low temperatures due to competing electronic interactions. This NMR/NQR study reveals the microscopic structure of magnetically ordered phases and characterises the quantum phase transitions (QPTs). Both systems can be driven through quantum critical points (QCPs) using an external magnetic field, with similar effects observed in other systems under hydrostatic pressure or doping. Near the QCP, strong quantum fluctuations lead to the formation of quantum critical matter, hypothesised to have a universal description. With two distinct cerium magnetic moments in CPS, antiferroquadrupolar (TQ = 470 mK) and antiferromagnetic (TN = 250 mK) orders are observed at low temperatures. Neutron scattering research links the magnetic activity to cerium moments at the Ce(8c) position, and CPS shows a Kondo-breakdown QCP, where magnetic order suppression coincides with Fermi surface reconstruction. We investigated CPS using 105Pd NQR and 29Si NMR, determined the quadrupolar coupling parameters νQ and η, and found no conventional magnetic order down to 70 mK. However, temperature-dependent relaxation rates suggest the presence of two Kondoscreening energy scales, with no sign of quantum criticality at low temperatures, implying an unobserved magnetic order between Ce(4a) moments. BoNO, an organic biradical, forms an effective S =1 Haldane state, confirmed by bulk magnetisation and X-band EPR measurements. We investigated its magnetic field-induced long-range ordered (LRO) phase using 1H NMR, determining critical exponents consistent with a 3D-XY antiferromagnetic QPT (ν = 2/3). In the gapless phase, nuclear relaxation rates align with the Tomonaga-Luttinger liquid model. The staggered magnetic moment evolution in the LRO regime matched the mean-field and Quantum Monte Carlo (QMC) predictions, though slight discrepancies suggest magnetostriction effects under an external magnetic field. Finally, we compared BoNO with other field-induced Bose-Einstein condensate systems and used the standard scaling relations to describe quasiparticle behaviour in the quantum critical region.