Time-Life Records began issuing a series of three-LP box sets in 1970 that recreated the hits of the swing era. Most of the recordings were made by Billy May and His Orchestra, with some sets featuring tracks made by Glen Gray and a modern version of his Casa Loma Orchestra. All arrangements followed the original hits very closely.
Each box set (there were 14 of them) included a 64-page book. Despite the fact that these are not the original recordings The Swing Era series proved to be enormously popular -- one of Time-Life's biggest sellers. The records were pressed by Capitol Records Special Markets division and the pressings and stereo quality are top of the line.
Below is May's version of the Erskine Hawkins hit Tuxedo Junction, taken from the volume covering 1940-1941.
These Time-Life big band recreations were reissued at least three times in their entirety -- twice on vinyl box sets, with slightly different covers in the mid-1970s and entirely new covers later in the decade, and on CD, beginning in 1999. The track listings for the CDs varied from those on the LPs and the covers looked like this:
Reasonably priced vinyl box sets are easy to come by online. They also seem to populate thrift store shelves fairly often. The CDs, however, are harder to come by and seem to be quite pricey. These recordings haven't been marketed as downloads under The Swing Era title, but it's possible they're available on other compilations.
Here's another sample of the Swing Era series, this one taken from a CD. This time it's the Glen Gray Orchestra recreating Andy Kirk's Moten Swing.