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For those of you who are wondering whether it's worth it or not to drain the block, here are some before and after pictures showing the amount of coolant drained from the radiator and the additional amount drained from the block:
Radiator Only
Radiator and Block
Getting at the block drain plug is no picnic. It's much easier, however, if you remove the oil filter first. You don't have to drain the oil - just let the car sit for awhile, and all the oil from the filter will drain back into the pan. The drain plug is 19mm. On my 2001 Civic, I used a 1/2" drive flex head ratchet, about 16" long. For some reason, that wouldn't work on my girlfriend's 2004 Civic, so I used a 3/8" drive flex head ratchet, about 11" long. In either case, you'll want a fine tooth ratchet, as there's not much swing to be had. The plug is torqued pretty good, so you'll need to lean on it. I found it easier to remove using a 6 point socket. Oh, and when that plug comes out, you'll get a good drenching. My advice is to put a large pan underneath, and back out the plug very slowly (don't remove it yet) until you get a steady stream of coolant, then go have lunch.
First post here, I believe - currently have a 2001 LX with 28,000 miles, inherited from my Mom, who drove about 10 miles/week. Also, daily driver is a 1996 318ti with 213,000 on the clock. Admittedly, the Civic only leaves the garage once or twice/month, it's main function being to provide transportation while I work on the 'ti.