How do you remove the alternator on a 1999 Mazda Miata?

I just replaced mine. The process is pretty straight forward. Obviously, step one is to disconnect your battery. I wasn't sure if the alternator would come up through the top for removal, so I opted to remove the splash guard from the bottom front of the engine. I then jacked the car up and it gave me great access to some of the work from underneath. The alternator was easily removed through the bottom. There are two electrical connections at the alternator. One bolts on from the battery, and one is a plugin connection that requires you to push the tab in before pulling the connector off. You can decide for yourself whether you want to do this while the alternator is bolted up or whether you want to loosen the alternator to have better access to these connections. I personally took the top bolt out and loosened the bottom bolt before removing the electrical connections. NOTE: my new alternator (rebuilt technically) came with an insulating block that did not work with the battery cable connection, so you will want to check this before returning your core in case you need to take the insulating block off your old alternator. The alternator is held on by two bolts. The top bolt is part of the tensioner, which uses, thankfully, an old style bolt system to tension a separate alternator belt. Once you remove the top bolt the tensioner can be removed by sliding it towards the rear of the car through the slot it sits in. The bottom bolt has fallen prey to what I consider an engineering oversite. The bolt threads out towards the back of the engine, and because of this, you have to remove the stiffening arm that sits right behind this bolt. Fortunately, the stiffening arm is held on by three bolts, all of which are easy to get to. Once this arm is out of the way you can remove the bottom bolt. Reassemble in the reverse order, connect your battery, reprogram your radio, etc. Your fault codes are going to be cleared, so if you needed this information for any reason, get it read before disconnecting your battery.