So I remember in Pokemon using False Swipe, which would leave 1hp if it was a killing blow, to capture Pokemon that were lower level. So far, I've found 2 methods that are effective for myself in capturing lower level pets without killing them.
First is to use random appropriate-level pets when fighting in the wild. This is not always ideal if you feel like grinding some levels with your main team while hunting rares. I always felt I wanted to include a decent high level pet handy to hunt rares with.
Another method I found is to use the ability Frog Kiss on my Mojo. This ability is also found on other frogs, notably Small Frog. The reason I use this ability is because it does small damage, and effectively lets you weaken the pet's health into capture range without overkill.
So anyone else have any useful tips for rare hunting without accidentally killing the pets? I'll be keeping my Mojo handy and I highly recommend training any frog for this useful ability.