The Romans wrote about history and recognized monuments from past eras both at home and abroad. But it occurs to me that I have never heard of them digging anything up — I fail to recall anything that resembles archaeology done by the Romans or their contemporaries. Does the Roman literature mention any kind of archaeological excavations or comparable attempts to physically unveil history?
There is reference in Plutarch's Moralia: the Genius of Socrates to the deliberate opening of a tomb.
Therein they discovered:
"a bronze bracelet of no great size and two pottery urns containing earth which had by then, through the passage of time, become a petrified and solid mass"
and a bronze tablet "with a long inscription of such amazing antiquity that nothing could be made of it ... but the characters had a peculiar and foreign conformation, greatly resembling that of Egyptian writing."
- They also discovered that the body of the original occupant had been replaced by a stone.
Although the opening of the tomb appears to have been deliberate, it was with the intention of removing the remains to Sparta (from Boeotia), rather than to learn something about history. But I think the bronze tablet, with its "inscription of such amazing antiquity", which was passed on to Egyptian authorities for study and hopefully translation, makes this a case of 'accidental archaeology'.
I know that Plutarch wrote in Greek but he was a Roman citizen, undoubtedly read by (educated) Romans, and you seemed open to accounts of "contemporaries", so I hope this passes muster!
The passage can be found at: Plutarch, Moralia: the Genius of Socrates, 577D-578B. The translation I have used is that of Phillip H. de Lacy and Benedict Einarson (1959).