If it is set in a mortar bed like Sombreil said, it would be very hard to selectively remove it. I would consider filling in the missing area with something compatible and letting it be what it is. It would have to be done with a lot of thought, but I have seen it done.

There is a Beaux Arts hotel in my city that has a marble mosaic floor in the lobby, and at the time the hotel was renovated (late 80s?) the marble mosaic was not available, so there is infill of tile that is compatible. Now, of course the marble mosaic would be available again. It works in this commercial space, perhaps it could work in your kitchen.

How beautiful! What a great find!

Here in Florida, that is called "Cuban Tile" due to the prominence of the craftsmen who made it being from Cuba.
It was very common to find on porch floors, kitchens, bathrooms and as the tile surround for fireplaces.

Do not try to use products from Home Depot, Lowes, etc. as they generally are clueless as to what to use as many products can lighten the pigments used to color the tile. I ended up using a mild soap/water to clean my tile then a mixture of 50/50 boiled linseed oil and mineral spirits to revive the color and sheen.

There are some companies in Miami that still do this craft. I would start my research in that direction to get recommendations as to how to restore.

Good luck!

Yes, my BF was concerned about just using "anything" i.e.; going to a large commercial store such as Home Depot for advice.

I'm trying to do some research online to see if I can find anyone near my area (NJ/NY) who can help.

You should probably contact the folks at
http://www.villalagoontile.com/

They know a lot about cleaning and preserving encaustic tile.

Funny you should post that - I already contacted Villa Lagoon. They are probably going to be able to recreate the tile for me so that I can finish off the area in the kitchen where the tile is missing. We left it off that once my contractor takes a look at it next weekend, I'd send photos for them to assess the situation.

Great customer service - they got back to my email within minutes of me sending it.

What's happening with your floor? the floor I would kill for? I read on another thread the replacement cost was a bit steep.

Sadly, we can't keep it now.

For one thing, I found out the cost of matching the tile to the area which does not have it, would be approximately $2000. I never expected that, had no idea new encaustic tile was that much money let alone that wasn't even the price to exactly match it, just for some other encaustic tile in general - I never even got around to asking how much it would be for a special order. Once I found out the price of their stock line, that was that.

Aside from that anyway, when demolition began it really dinged up the edges of the existing tile rather badly. I had to take a hard look at the situation and when my BF even admitted that he felt it might be the wrong move to try and salvage it (he, I think, was more in love with it than I) I finally admitted defeat.

I am now on a quest to try and figure out the best material to float over the floor. I've been told that laying regular ceramic over is the easiest method but I really would prefer a wood floor to match the rest of the house. So - not sure yet what's going to happen.

Bummer for sure.