Anime with little dolls which look like girls in mecha suits fighting as commanded.
I once watched a teaser for this anime. I don't know if they were 'micro girls' or human-like dolls/robots dressed in mecha suits. But they were fighting each other willingly, I think, just like in Pokemon or Medabots. Seems to be a real nice anime; never saw any other like that one and haven't come across it again. Would love to watch it, seems really cool.
Could this be Angelic Layer (2001), AKA Battle Doll Angelic Layer...?
From Wikipedia:
Angelic Layer (Japanese: エンジェリックレイヤー, Hepburn: Enjerikku Reiyā) is a Japanese manga series created by Clamp. The manga was published in Japan by Kadokawa Shoten, and in English originally by Tokyopop, but has since been re-licensed by Dark Horse Comics. It was the group's first work using a significantly pared down style, which lowered emphasis on detail and accentuated posing and gestures. It would later be repeated in series like Chobits and Tsubasa: Reservoir Chronicle.
The manga was adapted into a 26-episode anime series produced by Bones titled Angelic Layer: Battle Doll (機動天使エンジェリックレイヤー, Kidō Tenshi Enjerikku Reiyā, lit., "Angelic Layer: Mobile Angel") which aired on TV Tokyo from April 1, 2001 – September 23, 2001. Seven volumes of videos were released by ADV Films on VHS and DVD in 2003. It was re-released in 2005 as a five volume box set. North American publisher Dark Horse Comics re-releases Angelic Layer in omnibus format in 2011. Sentai Filmworks will re-release the series under their Sentai Selects label on November 24, 2015. Anime Limited announced they would release the series in the UK in 2018.
From IMDB:
A young girl battles her way through the exciting games of Angelic Layer, where players fight with tiny robotic dolls to win the national championship.
It does feature Pokemon-style tournament battles between mechanical dolls.
I can think of two very similar anime that match your description, both of which involve tiny human-like robot girls who are owned by humans and fight each other for sport.
The first to come out (2012) was Busou Shinki.
It featured four main shinki (its word for the robot girls) and their male owner, in a world in which shinki are very common and owned by almost everyone, with there being established tournaments for shinki fights, though most of the episodes aren't about fighting but instead slice-of-life plots. One of the main plot points is that of the four main shinki, one of them has only recently arrived and is more committed to professional fighting: she often has personality clashes with the owner's original three shinki who are more laid back and prefer only to use their mech-suits to help out (or not - lots of slapstick comedy) with the slice-of-life stuff.
The spiritual successor to Busou Shinki (coming out in 2017) was Frame Arms Girl.
In Frame Arms Girl only the main character owns robot girls as she's being sent prototypes to try out. A new frame arms girl arrives every few episodes and all of them enjoy fighting, so most of the episodes include fights between the various girls as they test each other out.
I think this might be a mecha anime called Str.A.In: Strategic Armored Infantry. The show has dolls as aliens and a time-traveling brother that fights against the protagonist sister.
The Union's strongest force is made up of mecha called Strains, short for Strategic Armored Infantry, operated by pilots called "Reasoners". In order to become a Reasoner, a potential pilot must have a Mimic, a machine fused with brain cells taken from the Reasoner before birth - thus, if the Mimic is damaged or destroyed, it cannot be replaced. The Deague do not possess Strain technology, but instead utilize swarms of small automated attack fighters called Tumors.
