I really doubt Honda (or anyone else) has an actual sensor(s) onboard the vehicle for testing the actual oil. Most likely what they have is the computer keep track of ignitions, idle times, maybe temps (outside and engine), rev's, time spent at rev's, etc. At then derive when you should change based on that.
As previously mentioned, the only way to really
know is to get your used oil tested and have them give you a TBN number. Then, based on that, and assuming your driving habits don't change much, you can determine how long you can push your oil.
Your Honda probably spec's a xW-20 oil. If it does, there are no synthetics, save for
Amsoil 0W-20. or (possibly)
Mobil-1 Extended Performance 5W-20, that will get you out to 15k mi./1 yr.
safely.
For either of those, you're going to need to a.) use a filter rated for that distance (think the Amsoil Ea line of filters...they're Donaldson's, top notch), or b.) use a decent filter (like a Wix/NAPA Gold) and change the filter & top off the oil at your current recommended change interval...b.) being the safer alternative.
You need to pick one of those two oils, and run it out and take a TBN test before you start getting into some truly long mileage's/time intervals. Once you go past the oils ability to neutralize the acid buildup in the oil, you'll start eating up the soft metals (think bearings...bad...) in your engine.
Oh...and it goes w/o saying that if you can't prove you changed the oil on the manufacturers guidelines, and you have an engine failure related to the oil system.....No warranty for you!
Chuck