My knowledge is three kingdoms (190-280) with some knowledge of the Han that came before it.

Not much, at least while the husband was alive. On property, courts were not keen on Emperor's having more property, parks and the likes, they kept the Emperor's restrained on such matters and were very quick to complain about expansions. Attempts to get around that via the Empress would probably have not gone down well. In terms of ceremonies, nothing comes to mind bar investiture as Empress but, for example, Han ceremony it isn't always clear if Emperor's themselves always took part.

There was a divide between what the Emperor managed and what was considered appropriate for a female. A good Empress was restrained, knew the right arts like music, helped the Emperor choose the right concubines to favour, filial. They could manage the household for good or for ill, Wei claimed Cao Pi's first wife Zhen helped manage the harem and cultivate them, Liu Bei's long-serving battlefield concubine Lady Gan often took charge of the household (Liu Bei tended to lose his wives), Liu Bei's later marriage to ally Sun Quan's sister (which was a disaster) saw her take charge of his household including the education of his only (at the time) natural son Shan (then attempt to kidnap him). The elderly Wu Emperor Sun Quan urged Lady Yuan (daughter of the failed Emperor Yuan Shu) to become his Empress so she could take control of his increasingly divided and out of control household (two of his daughters Luyu and Luban were backing rival claimants for heir among his sons), she modestly/wisely dodged out of that one.

If the Empress had power behind the scenes, this wasn't something the historians highlighted and would have raised alarm if too obvious. Cao Pi's future Empress Guo acted as a political adviser when he manoeuvred to be the heir of his father but we don't get a single record of that advice. She has also been implicated in the death of Zhen. When Guo became Empress, I can not recall a single piece of advice she gave in political sphere other than, when threatened by her mother-in-law Bian with being deposed, she put her voice to the pleas to get Cao Pi to spare long-serving general and kinsman Cao Hong over a long-standing grudge. The concentration of the records of Guo as an Empress is her management of the harem, acting properly when Cao Pi was away on campaigns (and then her fall under Zhen's son Cao Rui when she was Dowager).

The Cao Hong incident is an example of where the real power for an Empress could be. When your husband was incapable or dead, then the power came to the Empress Dowager. If she had a son then she was looking after his interests, if she didn't have a son then she got to select the new Emperor. With the eunuchs in the palace and her family acting as agents on the outside (though Wei took measures to combat this, it made them vulnerable when they did have a child Emperor), either the family (like the Liang's) or the Dowager herself could, in effect, rule. Even, as Emperor An among others discovered, they were an adult the Dowager could, with enough skill and backing like Dowager Deng Sui, remain in charge (the Han had a few Emperor coups against their regents and Dowagers). Even if the ruler was an adult and fully in charge, an Emperor had filial obligations to Dowager even if not her mother so Guo may have been Empress but Pi's mother Bian had the power in that dynamic.

In the three kingdoms, Sun Quan's mother Lady Wu (though not an Empire at the time) ruled in his early years following the death of his brother Sun Ce, deciding foreign policy and chief ministers (which led to some awkwardness between Sun Quan, when he grew up, and the two said unrelated ministers Zhang Hong and Zhang Zhao). Dowager Guo, wife of Cao Rui, may have had little practical power due to Wei policy but her position provided the legitimacy for the Sima family as they whittled down the Cao power, anyone rebelling against the Sima's also claimed her support and she used what natural authority she had to make life difficult for the Sima's. Sun Quan's last Empress Pan, as Sun Quan became fatally unwell, looked at what she could do as Dowager and was murdered by senior but unnamed members of the court to prevent her from becoming Dowager.

While there were able and formidable wives of warlords and Empresses, the real power lay in being a Dowager when their husband passed away rather than being an Empress.

Sources: Empress and Consorts by Robert Joe Cutter and William Gordon Cromwell

Fire over Luoyang: A History of the Later Han Dynasty and A Biographical Dictionary of Later Han to the Three Kingdoms 23–220 AD by Rafe De Crespigny