I think in either case I'd put in a solid threshold ... marble or other material. There are pre-made ones that accommodate different levels of flooring.

Thank you for the suggestion, wi-sailorgirl. How exactly does the carpet connect to the threshold?

Gosh, I have no idea! Never even thought about that, to be honest. I hope someone knows the answer.

I have a sneaking suspicion that you'd cut the carpeting away there, attach the threshold to the subfloor, and put down new carpet tack strips around it, but I'm totally guessing.

It doesn't. You run a tack strip in front of the installed threshold, and stretch the carpet to the tack strip.

Another possibility would be to "turn" or "tuck" and tack it (basically making a "sideways hem") right to the edge of the tile. One other way would be to use an "insert" strip. It's a channel strip with a tack edge that you stretch the carpet to, and then there's a vinyl "T" shaped insert that pops into the channel, and caps over the edges of the carpet and tile. ANY of those will work, as well as using a wood threshold instead of marble.

My preference, though, would be for the marble threshold. But I'm kinda biased. :-)

I found this (John Bridge) tutorial which sounds very similar to the "tuck" method you describe. Is it?

While I love marble and wood thresholds in many applications, I'm not certain if it will work for me. But I'm willing to investigate. Also, can you tell me where I might find these "insert" strips to look into? Essentially I'm hoping to find something that bridges the two materials and prevents people from tripping or the carpet from fraying.

Thank you for the expert advice.

This is the insert, installed:

You can get it at any carpet showroom, and most likely at Lowes or Home Depot's flooring departments.

That looks perfect. Thank you for the picture and the suggested sources. I'll check out Home Depot or Lowes on my next trip there. If I don't find one, I'll start looking up local carpet showrooms. I really appreciate all of the time and knowledge you share with us on this site, Bill. Thanks!