The Check Engine Light on a Miata indicates there is a problem that should be diagnosed. It can be as small of a problem as not tightening the gas cap to general misfires that may cause subtle, long-term damage.
There are two ways to achieve this:
You can clear codes with an OBDII scanner that has this feature. You can purchase one for roughly $80-$120 and it takes 5 minutes, or you can go to a repair shop and they will clear it for you for a minimum of $40. But they will warn you of the problem and attempt to make a diagnosis.
The quick and dirty way is to simply disconnect the battery, pump the brakes to remove all residual power, wait for a few minutes and reconnect. It will remove the codes, but it will also cause the car to relearn your driving habits and environment. For the first few miles, the car will act differently than you are used to.
Note that if there is still a problem, the light will come on again after it completes a cycle of tests that will run after a few drives and miles on the car.
Also, depending on your local smog laws, if you have disconnected the battery to remove erase the problem codes and the vehicle hasn't completed its full round of tests, it will let the smog technician know if he/she checks for that and the test won't be valid.
The 2002 Mazda MX-5-Miata has an inline 4 engine.
The 2009 Mazda MX-5-Miata has an inline 4 engine.
The 2004 Mazda MX-5-Miata has an inline 4 engine.
The 2003 Mazda MX-5-Miata has an inline 4 engine.
The 2007 Mazda MX-5-Miata has an inline 4 engine.
The 2001 Mazda MX-5-Miata has an inline 4 engine.
The 2011 Mazda MX-5-Miata has an inline 4 engine.
The 2013 Mazda MX-5-Miata has an inline 4 engine.
The 2014 Mazda MX-5-Miata has an inline 4 engine.
The 2008 Mazda MX-5-Miata has an inline 4 engine.
The 2012 Mazda MX-5-Miata has an inline 4 engine.
The 2005 Mazda MX-5-Miata has an inline 4 engine.