 If you liked Chouyaku Hyakuninisshu: Uta Koi. |  ...then you might like Shouwa Genroku Rakugo Shinjuu |
Both period pieces that look at Japanese culture. Probably completely boring to anyone not interested in Japan.
One, about poems, the other about rakugo. Both heartbreaking in their own way. If you watched Uta Koi and want another story filled up with angst, that feature tragic love stories and very adult and mature characters, then please watch Rakugo Shinjuu (same thing the other way around).
Both are josei period dramas about old and unique forms of Japanese art (rakugo or short poems). Both embed to a significant extent the actual content of those arts into narrative. Both are about how performing the art influences one's everyday life, dealing particularly with romance/friendships part of it. Uta Koi however is slightly postmodern, its episodes vary in tone and include elements of absurd comedy while Rakugo tells a continuous and somber story.