Depending on where you live you might be able to find a local brewery that's doing some sort of a recreation of an older style. In the Massachusetts area Pretty Things Beer & Ale Project does a series of 1800s English ales called Once Upon a Time. Beer historian Ron Pattinson helps them design all those recipes based on his research, so they should be fairly accurate. Dogfish Head has a similar series called Ancient Ales which are best-guess recreations of VERY ancient middle eastern and asian beers based on archeological evidence...studying the chemical residue left on beer containers.
You might be able to find some recreations by Brouwerij de Molen who also tapped Ron Pattinson to consult.
Traditional Belgian styles are unlikely to have changed significantly, so those are an option. The smaller niche styles don't evolve as quickly, though the methods will be updated so they won't be as accurate as deliberate recreations. Saison Dupont was mentioned. Fantome springs to mind as well. Certain sour beers like Faro or Gueuze Lambics should be close, but avoid the fruity ones. Gose and Berlinerweisse might fit as well. A lot of those European sour brewers have been doing things basically the same way for like 500 years.
If you can find anyone brewing a Sahti that would be an interesting adventure. I've also heard rumor of a few recreations of styles like Gratzer/Grodziskie, I think New Belgium might make one...
On the smaller scale, if you're really interested see if you can find Frank Clark or Bob Grossman at a conference you might be able to get them to let you try a historic recreation beer, they generally work in the 1600s-1700s. Frank Clark works as a food historian at Colonial Williamsburg so he should be easy to track down. But I warn you, you probably don't want to actually drink the majority of that stuff. Brewing was very different back in the day and a lot of their beers are pretty foul to modern tastes. Differently prepared sugars and odd herbs and spices. Stuff like boiling molasses until it literally lights on fire then fermenting it...kilning grains until some of the kernels straight explode and burn. And let's not even get into stuff like cock ale, which had a parboiled rooster added during secondary fermentation.
Sorry, that got ramble-y, but the gist was: Pretty Things Once Upon a Time if you can get it. Anything involving Ron Pattinson. Dogfish Head Ancient Ales. Traditional Belgian Saisons. Sour Beers: Lambic, Gueuze, Berlinerweisse, Gose, Gratzer, Flemish Red. Frank Clark might let you drink really gross-tasting things that were technically considered beer in Colonial-era America.