Arya Nagarjuna as a scholar, only dispelled the arguments of the reificationists or the annihilationalists. In doing so, he conceptualized sunyata- sunyata is itself sunya (sunyatasunyata). It is merely an analytical tool (certainly of the gretest importance and very profound) to go beyond the obstructs of conceptual thinking- go beyond thinking to the direct experience of reality of mind-body phenomenon in its entirety.
Arya Nagarjuna reached the "perception of emptiness" by the same way as all Budhhas, Boddhisattvas, Arihants have reached and we can reach- by the technique of Vipassana- by the direct experiential insight into the phenomenon of mind-body, which is empty of all conceptual constructs.
But I am sorry to say that I myself do not know of any scrpitures which discuss the meditative experiences of Arya Nagarjuna.
EDITED- It may help you to look at Tsong Kha pa's "The Great Treatise on the States of the Path to Enlightenment". In fact, if you already have not, you may try searching through the Lamrims. Although, I doubt whether it particularly deals with an account of Arya Nagarjuna's meditative expriences. But they may help you make correct inferences and deductions (much Like I have done in this answer).
EDITED (2nd)- It will be very useful for you to look at Arya Candrakirti's The Entry into the Middle Way. In some translations, Stage one "The Joyous" is associated with the direct perception of sunyata.