Unfortunately, this is not easy, and it is our understanding that the FAA really does not intend for these installations to happen. Your mileage may vary, and we DO NOT provide support towards efforts to install our avionics in type certificated aircraft. Our avionics are intended for use in homebuilt, experimental, and light sport aircraft.
Here's the full story as we understand it (and were not certification experts, so some of this might be wrong):
The FAA wants to see certified avionics in certified aircraft, period. It doesn't matter if you only want to use it as a backup, even if you don't touch any of the existing avionics. The FAA has several overlapping approvals that need to be in place to get "certified". These include supplemental type certification (STC), meeting TSO standards, receiving PMA authorization, and so on, that need to be sought by the manufacturer.
We do not currently have plans to certify our avionics (though some day, who knows).
For "major modifications" that are of limited quantity, such as "one-off" aircraft modifications, the FAA has the 377 field approval process which is administered regionally (by the FSDOs). To get a 337, you are supposed to do fairly major engineering analysis that effectively substitutes for a certification effort when one is not practical. The FSDO and people that they delegate their authority to are responsible for approving and rejecting 337s
Our understanding is that the federal FAA folks do not want to see experimenntal avionics, particularly EFISes that incorporate primary flight instruments, installed under 337. How firm this position is, and how they communicate this to their regional FSDOs is unclear to us.
From time to time, we hear from people who claim to have had success gaining 337s for EFISes in their aircraft. If they've received approval from a FSDO or other authorized representative, our understanding is that the installation is then legal. Further, if the FAA chain wanted to have the 337 pulled, such an enforcement action requires proof of an unsafe condition.
We have also had reports from customers that have been told NO in very concrete terms by their FSDO or other FAA representative, citing the above reasons.
We do not keep records of anyone that claims to have obtained a 337, nor do we have any information on what those people maybe have done to be successful in their efforts.