We know that Kirk meets Picard in Generations. And that Scotty mentions an "Admiral Archer" in Star Trek (2009). Does Archer ever meet any other Enterprise captains?
Depends what you consider to be a "Captain" of The Enterprise.
It sounds weird, but bear with me. T'Pol and Tucker have both temporarily acted as Captains on the Enterprise. In addition to this, their son, Lorian, from an alternate timeline, was also Captain of the Enterprise until he went back in time and changed history. Captain Archer has certainly met all three of these people.
However, if you limit it simply to people that have been appointed Captain of The Enterprise, then none of the above count, in which case we have to move onto The Enterprise NCC-1701. The captains of this vessel are (in order): April, Pike, Kirk, Decker and Spock. After that we have The Enterprise-A,B&C before moving onto Picard's era. There is nothing to suggest that Archer has met any of these Captains, and while it is possible for him to have met the likes of April or maybe even Pike, it is unlikely that he will have met anyone from Kirk onwards, since Archer was 121 years old when Kirk was born.
Each of these Captains, however, will know of Jonathan Archer, being the man who made the United Federation of Planets possible, and who was President of that same Federation for 8 years.
I also believe it to be quite likely that, as an Admiral, Archer would have had some say in who was appointed Captain of The Enterprise.
So, in short, Jonathan Archer has met people that have Captained The Enterprise, but as far as canon material goes, he has not met any person that has been appointed Captain of The Enterprise by Starfleet.
Jonathan Archer has once visited the Enterprise-J, but it is unclear if he met its Captain while on board:
DANIELS: You're on Enterprise. Enterprise J to be exact, a distant relative of your ship. We're four hundred years in the future.
[S3, "Azati Prime. From Chakoteya.net]
According to material seen on screen for Archer's biography (seen in "In a Mirror Darkly", using information from the "Normal" universe) he, "... died at his home in upstate New York in the year 2245, exactly one day after attending the christening ceremony of the first Federation starship Enterprise, NCC-1701"
Presumably, by that quote, Archer would've met Captain April, mentioned as the first captain of the Enterprise
There is, of course, the possibility that Archer met with a future Captain of the Enterprise (i.e. Cadet Kirk or a younger Spock) before they'd become Captain, but there is no source to support that.
Sources: Quote from on-screen text in "In a Mirror Darkly"
April was a former Captain of the Enterprise according to TAS: The Counter-Clock Incident
Christopher Pike was a former Captain, as mentioned in TOS: The Menagerie and TOS: The Cage
He met John Harriman of the Enterprise-B. Harriman has at least one non-canon novel about him, at the end of which he passes command over to Sulu's daughter. Another novel has him meet Captain Morgan Bateson, not long before Bateson's ship Bozeman ends up in the future and nearly collides with the Enterprise-D. In that same novel, Bateson ends up becoming the first captain of the Enterprise-E, before handing over command to Picard.