The on-line indexes are the result of the Library Of Congress digitization project. I was in the card catalog / main research room on a couple of occasions circa 2008-2011 when interns and college students were photographing both the index books and drawers of the card catalog. Wish they could've done this 20 years earlier!
I've had copies of the indexes before they went public (around late 2011) so I can harvest registrations before making my trips to Washington DC. Prior to having the digital indexes, I had to go to Yale University's Federal Depository library, where the have the hard-bound index books shelved in the stacks. Every state has Federal Depository Libraries, where all official publications printed by the U.S. government are stored.
The only method to retrieve the original copyright certificate denoted by the registration number is to have the registration retrieved from the LOC stacks. You can pay the LOC to do this for you - quite expensive now, $200 per hour, then a quarterly hour fee is charged after that. Or, you can visit the LOC and do so for free, once you are accepted as a LOC researcher (fill out forms, background check, and issued an ID card, which must be swiped or presented to a staffer when entering and exiting each room).
Prior to the 9/11 tragedy, I was able to roam about freely and take the elevator down to the large room where the bound books of original certificates were shelved, and look up registration numbers myself, without any hassle. I could pull and transcribe data for 100 registrations at a time in roughly 75-90 minutes. The LOC no longer permits anyone other than authorized staff members in that room, so the process to retrieve registrations is most restrictive, at least for my purposes, as I often need to access at least 100 per visit. Today, you have to key in the data on one of the bays of computers. Researchers are limited to no more than 25 registrations at one time (thankfully, I harvested 1000s of them before this rule went into effect). Once the data is keyed in and submitted, a staff member retrieves the bound volumes of registration numbers (500 certificates are bound per volume, so making sure you have the correct number, mistake free is essential). The wait can be anywhere from 15 minutes to longer than one hour, depending on the day, workload of staff, etc. The staff member wheels up the bound books on a metal or wooden cart, taking the elevator from the basement archive area to the fourth floor and wheels the cart into the room where you are waiting.
I've been doing registration harvesting since 1995, and have nearly 5,000 registrations documented. I did not miss too many, so anything that is a well-known garage-sounding or obscure track that was registered and you spot it in the digital indexes, I've likely got it here. My last trip back in mid-May to prepare for the new book tallied around 165 registrations. I still have some more to look up; I'll wait until I get enough of them to make another trip down to DC worthwhile. No way would I consider paying the LOC to do it.
Here is the circular with the fees charged by the LOC
http://copyright.gov/circs/circ04.pdf
