It may work to simply be able to click on an interceptor in-flight and select from a short list of behavior settings, such as "follow" (useful for chasing a UFO over water but keeping distance until it nears land), "assault" or "attack" (to try to shoot it down), "destroy" (In an attempt to blast it out of the sky, if a ground mission isn't desired afterwards), etc.
It would then also be nice to have a "guard" or "escort" option for following friendly transports to protect them and also to patrol near a player's base if the player thinks one of their bases might be attacked soon.
...And of course, also an option for sweeping areas looking for an alien base or other special (potentially plot-related?) activity.
As a final note, I think there is already an option to send a fighter back to home base if it isn't doing too well. (I admit I've been busy lately and haven't fired up the latest SVN version in a while.)
I'd think this would be easier to code than a complete mini-game that pops up.
EDIT: If pilots are ever added to personnel, (that could be hired/fired, have various skills, etc.) then a "eject" option would also be nice as a last resort to save a good pilot - whether or not a ground extraction mission would result would depend on if the pilot landed in a friendly territory (that supports the player) or not, or if the pilot landed in the middle of the wilderness - or even the ocean! (I could very well imagine a pilot surviving a *short* time after landing in the ocean, hoping for a quick rescue before their supplies run out.)
EDIT (Again!): If pilots were added to personnel, one of their potential skills related to quick-thinking and reaction could affect their chances of successfully ejecting automatically if they think their fighter is about to be destroyed (They are damaged badly and they see that plasma blast or whatever from a UFO coming at them with their name on it...)