Hmm... the only way to carry a sword the way the character is wearing it in the top image at that website is to actually attach the scabbard to the white coat, since there don't seem to be any straps or belts around his upper body. (Hooray for seemingly impossible character designs! It's a common problem in cosplay, sadly.) To do it that way, I'd sew loops onto the back of the coat, and attach the scabbard to those loops.
I don't have experience with belting ninja-style swords to my waist, but at the ren faires I've gone to, the scabbards that can be purchased with the swords traditionally have some extra length on the backside (the side that would be against your hip) of the scabbard, which you can fold over the belt and fasten with a (large and very secure) snap or button on the backside of the scabbard below the belt. (I'm not sure I'm explaining this very clearly - sorry!) Or else there's already a loop on the backside which you can slide onto a belt - think of the back of a cell phone belt pouch.
One thing to note about attaching swords at the waist, though - depending on how well they're balanced and the angle the scabbard is attached at, they may flop around all over the place and knock against your knee as you walk if they're ONLY attached at the waist. The blacksmiths I've bought from usually make their scabbards with another strap to be fastened around the leg above the knee to keep it against the leg, which works quite nicely.
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