Thank you for the image and for your patience.
The McKinley Tariff in 1892 decreed that all objects have a country of origin stamp on them.
From 1892 on items from Japan went from characters or no marks to at least having the word Nippon on them. Nippon is the Japanese phonetic word for Japan. Eventually they dropped “Nippon” and used “Japan”
As a rule of thumb, objects from Japan that have the country of origin “Japan” stamped on them, mean they were produced around 1920. “Made in Japan” stamp starts a little after circa 1930’s, briefly followed by “Made in Occupied Japan” from 1945 - 1953.
Thus your vases, with the word “Japan” in the mark date to circa 1920.
The green stamped mark with a wreath under a cherry blossom indicates that TN is actually a subsidiary of the Morimura Brothers who are the owners of porcelain export giant, Nippon Toki Kasha Company, otherwise best known as Noritake. The flower is actually 5 conjoined letters “M”.
The TN stands for the makers Tame & Nakamura.
The handwritten cartouche mark in characters essentially states the Nichi Hon Nippon Shimada Zo Tame & Nakamura Moriyama. Although referred to as satsuma, it is kutani palette.
These pieces were intended for the export market, generally the destination was America.
The decoration on the pair are hand painted and depict an idyllic summer day taking a small boat ride to little islets in lake under the gaze Mt Fuji.
The is from the Taisho period which followed the Meiji Period (in the Western world, a little bit like the Edwardian era after the Victorian era).
There are lot of Japanese export wares currently available on the market and the supply is
exceeding the demand currently.
Since the vases are not mirror image, you actually have 2-of-the-same-kind and not a matched pair. A matched pair would be mirror image to each other.
On today’s market, the vases could sell for a high average of $60 - $80 each at auction. The suggested insurance or replacement value is $175 each.