Remember an Miata engine is nothing more than an air pump that has a system to ignite a fuel to keep it spinning. The easiest way to boost your horsepower for the Miata is advance the initial timing a little. 14 degree before instead of the stock 10 helps with about 2 more HP and also moves the power band lower in the RPM range by about 400 rpm.
A replacement muffler for the Miata can give you another boost of 5-10 horsepower above 6000 rpm. The Borla stainless steel system for the 1.6 because is quite good as it is relatively quiet at idle, it is very light weight and will never rust. For the really budget conscious, a generic 'turbo' muffler (cost about $60) can be installed in place of the OEM, but you'll still have the restrictive mid-pipe in place.
Airbox mods can shorten the intake tract for better throttle response and reposition the intake to breath outside ambient air instead of the hot underhood stuff. The problem is that they typically do not add any horsepower in a 1.6, they just help keep from losing any. What I mean is that they aren't really increasing flow because the flowmeter is the real bottle neck and, while the cold/dense air is a good thing, it is only making up for the fact that the stock motor can't breath. The flowmeter is very restrictive and limits HP above 6000 rpm, replacing it eliminates the bottleneck.
This change will require custom intake plumbing. This is a good thing since you can now create that shorter cold-air system and really take advantage of it. If you do replace the factory intake plumbing with an aftermarket or a DIY system then make sure to keep the (anti)resonance chamber. It has been dyno proven to provide 4 ft lbs of torque from 3000-4000 rpm. If you need more horsepower above 6000 rpm, an aftermarket header can provide another 3-4 peak HP.
The Miata OEM header is better than most OEM exhaust manifolds but it is not tuned and has lots of restrictive welds and crimps while most of the aftermarket Miata headers have equal length, crimp free tubing. You probably won't notice any HP improvement until after 6000 rpm with a header. There are three places where the OEM header is restrictive because of welding and fitting. The head flange, the inside of the collector, and the downpipe flange.
Both flanges are welded on the inside and really restrict diameter and flow. The tubes are crimped down to nearly 1/2 their diameter and it has lots of welding protruding into the exhaust flow too.
Now, with the above mods, the motor can breath and is letting more air into the motor above 6000 rpm. More fuel is needed to keep the fuel/air ratio at optimum at WOT since the factory WOT settings are fixed (open loop) and do not take into account the Miata O2 sensor. I do not recommend 'chips' for the 1.6 motor since the 1.6 Miata ECU does not have a replaceable chip to program, the values are hardcoded into the logic.
It is a variable rate of gain model so it can be set to change the fuel pressure at different vacuum levels. I went this route so that only the WOT fuel was altered and not idle or mid throttle, where the O2 sensor will compensate if needed. I increased the WOT fuel pressure from 43.5 to 50 psi based on my fuel/air ratio gauge readings. But more fuel will keep you from losing any of your torque gains.