In the heavy-fermion metal YbRh2Si2, quantum criticality at a suppressed antiferromagnetic order is governed by the interplay of local magnetic moments and itinerant conduction electrons. We demonstrate how this can be investigated by a new experimental approach that enables the observation of electron spin resonance (ESR) across a broad range of frequencies and fields at very low temperatures. This allowed us to cover a large part of the phase diagram from the paramagnetic Fermi-liquid phase to the phase with antiferromagnetic order and including the quantum-critical regime. Both the ESR g-factor and the linewidth present distinct behaviors in these three regimes, providing further insight into the physics across a quantum critical point. Notably, when cooling down at a field directly towards the quantum critical point, both g-factor and linewidth continuously decrease. Furthermore, we observe a very good matching of the g-factor behavior upon field-tuning and temperature-tuning towards the quantum-critical point. We analyze and discuss the results in the context of present theories on ESR in strongly correlated electron systems.