Help to ID Ceramic Chess Set

This chess set has been in my family for at least 40 years, and some of the pieces are getting a bit chipped up.  I really like the size and design, and would love to replace them if possible.  King base is approx 1.4" wide x 3.85" tall (they are on a 2" square board)

No clue. Replacements might be non-existent. I would consult a ceramic restoration expert when you need to have them restored.

Looks like a version of the ceramic Medieval sets from Duncan although they are slightly different than any Duncan set I have seen. 

You could look on eBay to see if there are any there. 

I can help out here. Here's what you do. You can apply air-dry clay to cast molds for chipped noises and debris, Note: (It may not look the way it was originally was, but do your best to your liking.) Use cue tips to lightly dab on to the clay to remove any finger prints that may show. Wait for 10 minutes to dry midway, then get the best type of paint you can find to match the pieces you're working on. Note: (This may take 2 or more lairs.) Finally, to match the glossiness, you'll need superglue and apply and let it soak into the clay, it'll take more than 1 ply for sure. Let set over night, by morning, there'll will be super glue access, use a exacto knife or utility knife to carefully remove the superglue access. For final touch ups, use extra fine point pens for details. And there you go, you refurbished your piece. Hope this helps.