Not as in her age, but at what time she originally lived as a human.

When you first speak to Serana and mention the Empire, it turns out that she'd never heard of it. She's also surprised that it's in Cyrodiil.

So it was prior to Tiber Septim's conquest and founding of the Empire.

When exploring a Dwemer ruin, she may say "I always wondered what the dwarves actually looked like. I hear they're like elves, but with beards."

Which means they were already gone at that point. She doesn't belong to the period when Chimer were still around and at war with the Dwemer.

One more hint would be the line "Nordic ruins. Even older than I am. I wonder if the draugr are as gullible as they were when I was a girl."

In other words, Serana isn't as old as Hakon One-Eye or Gormlaith Golden-Hilt.

Speculate away.

if she is surprised about the empire existing, and it being in Cyrodiil, wouldn't that put her before the Alessian Rebellion?
was Cyrodiil not the capital of the Alessian Empire as well?

Yes, definitely.

so then.. that puts it as sometime in the early first era...

She's at least 4200 years old, given that she was sealed away before the forming of the Empire.

She also says "Is this a dwarven city? I'm surprised that they'd let it get this way." when approaching Mzulft.

Well she is older than 4,000+ years and I always wondered if maybe she was not the first vampire since the first was a female and her parents sacrificed her to bol to get their powers...

NS~

Lamae was the first vampire. Also a victim of Bal's fun.

This. So many times, this. Once I heard this line, I went to UESP and looked up when the Dwarves disappeared. It happened in 1E700, so she is 3751 years old, minimum. Add in about 20 years to get to advlthood, and she's at least 3771 years old. Possibly older; NPC age in Skyrim is very hard to determine, as someone who looks not a day over 30 can actually be pushing 60 (*pointed look at Delphine*). Add in the fact that she's probably had quite a few years as a Vampire, keeping her looking young when she should be old and grey, and I can easily believe she's at least 4000 years old.

Did the city of Solitude exist before the forming of the Empire? She doesn't know of the Empire but she knows of Solitude as she speaks of Castle Volkihar being off of it's coast.