Saucer Stone Piece Farming Guide
Aside from using Discs to unlock new Monsters, the only way for you to get a Monster that isn't a Mocchi, Zoom or Hare is to find saucer stone pieces and bring them to the Shrine. For anyone playing Monster Rancher 3 on an emulator or a device that can't swap discs you're stuck with having to find saucer stones pieces if you ever want a different monster. This guide is designed with these specific people in mind.
First off the most important thing to understand is that not every Monster finds saucer stone pieces. I raised three Mocchi Monsters and didn't get a single saucer stone piece. Once I started raising Zooms and Hares though I found about three Saucer Stone Pieces per Monster's lifespan. Aside from the one starter monster, the majority of monsters that I raised found saucer stone pieces.
The only place throughout the entire game that you can find saucer stone pieces is during Adventures which happen at the start of every new season. While you're exploring some areas occasionally Fletia will tell you, "I have a bad feeling about this, do you still want to search here?" This can mean multiple things, sometimes you'll find a Tech Bit, which taken to a Lord will get you a new skill. Other times though, you'll find a saucer stone piece like shown in my screen shot above.
Once you own a saucer stone piece you have no way of checking what it is or how many you have until a Rival shows up at your Training Location. In the list of options they give you select Trade and that will bring up a different menu which is shown in my screen shot below.
Trading for saucer stones at this point is pretty straight forward. There's different quality saucer stone pieces and you'll need to trade a piece equal to that in quality or a certain amount of pieces lower in quality to match the piece you want. In my experience none of your Rivals ever turn down a trade assuming you've matched the quality of saucer stone pieces.
In order to find better quality saucer stone pieces you'll need to raise your monster's battle rank by participating in the Tochikan Festa. As you move up in rank the chances of you finding better saucer stone pieces increases. In my personal experience, you'll start finding B quality saucer stone pieces once you reach A/B rank, S rank seemed to have no effect at all on the quality or quantity of saucer stone pieces I found for the first part of the game.
After I got 15+ monsters in my Encyclopedia I started to find A rank saucer stone pieces. Also it wasn't until after I got my first A rank saucer stone piece that I started seeing my Rivals carry them too. I'm not exactly sure what the trigger was but I was playing the game for a really long time prior to when I started to find A rank saucer stone pieces - I had raised about 20 monsters and went through about 100 years of in game time.
Each time that I raised a monster that I got to S rank but didn't take on any of the Great Four tournaments never found A rank saucer stone Pieces/never had a Rival I could trade for A rank saucer stone pieces. I'm fairly certain that one of the factors in finding them is completing the prerequisites to fight Ragnarox.
For anyone interested I have decided to include a list of monsters that I raised throughout the game with whether or not they can find saucer stone pieces; it's found below.
Hare: Finds lots of Saucer Stone Pieces
Zoom: Finds some Saucer Stone Pieces
Mocchi: Finds no Saucer Stone Pieces
Naga: Finds some Saucer Stone Pieces
Mew: Finds some Saucer Stone Pieces
Psiroller: Finds lots of Saucer Stone Pieces
Lesione: Finds some Saucer Stone Pieces
Baku: Finds some Saucer Stone Pieces
Jell: Finds lots of Saucer Stone Pieces
Octopee: Finds lots of Saucer Stone Pieces
Momo: Finds some Saucer Stone Pieces
Golem: Finds some Saucer Stone Pieces
Colorpandora: Finds some Saucer Stone Pieces
Pixie: Finds some Saucer Stone Pieces
Hengar: Finds some Saucer Stone Pieces
Suezo: Finds lots of Saucer Stone Pieces
Plant: Finds some Saucer Stone Pieces
Tiger: Finds some Saucer Stone Pieces
Suzurin: Finds some Saucer Stone Pieces
Beaklon: Finds lots of Saucer Stone Pieces
All the monsters I raised to test the rate they found saucer stone pieces.
Key:
Finds some Saucer Stone Pieces - I found one or two Saucer Stone Pieces during the monster's lifespan.
Finds lots of Saucer Stone Pieces - I found three or more Saucer Stone Pieces during the monster's lifespan.