Matriarchy in Name Only

In a fantasy world where women are considered to be the ruling gender and men are not, unlike the opposite that occurs in the overwhelming majority of civilizations in the real world, it raises some problems. Most writers do not have experience living in a civilization where women are the ruling class, and, as Most Writers Are Male, they can often be a little less mindful of what about female behaviour is naturally female and what is a sexist distortion. And if they're writing a Sexy Matriarchy for personal gratification purposes, they aren't going to really care. This is all very well and good, but it can cause Selective Squick for viewers who are seeking examples of genuinely assertive female characters in a believable speculative fiction setting.

That's when you get a Matriarchy In Name Only - a world where, despite women technically being in charge, the society contains very strong elements of a patriarchy. Maybe the men are supposedly treated as sex objects, but women dress in sexy clothes to impress their male slaves. Maybe the women rule by staying at home, and the men go out to actually influence the plot. Or maybe the main arbiters of power are women, but they all bow to a male demon that mind-controls their entire race. Whatever it is, it's clear that this world reflects our beliefs about gender. For those not used to this kind of analysis, it could be worth asking some of the following questions to a prospective "matriarchy":

Ignoring ceremonial titles, who gets their ideas realized in this society?
In practice, which gender has the most to choose from in terms of lifestyle?
Following that, who is representing the culture to the outside world as well as to the audience?
Is it possible to see the Male Gaze in how the society is depicted?
How do male and female characters actually value the genders and things associated with them?

A subtrope of Matriarchy. Can overlap with, or be the cause of, Sexy Matriarchy and Sexist Matriarchy. May also occur in Enlightened Matriarchies. Also includes societies that are supposed to be gender-equal, but show signs of still being skewed towards men. This can be done as a serious satirical point, and is not automatically sexist.

Can be a subtrope of the Rule-Abiding Rebel, if the author/publisher promotes the work as progressive/radical/controversial, but at heart, it's pretty conservative. Compare Faux Action Girl.

Examples of Matriarchy in Name Only include:

Anime and Manga

Infinite Stratos. We're told (kind of randomly at that) women rule the world because they're the only ones who can pilot the eponymous robots, but really, this being a Harem Show, that's mostly there to have the one guy who can pilot them surrounded by pretty girls.

Literature

The Wheel of Time—supposedly the societies would be dominated by women, but managed to be extremely sexist.
The dragons in Dragonriders of Pern—the golden queens are the effective "bosses" of the Weyrs, and no dragon will disobey her. Theoretically, this makes her the most powerful dragon in the weyr... but they're also the only dragon colour who can't breathe fire, and thus their fighting prowess is limited to the less dangerous lower levels of Threadfall (with their riders wielding flamethrowers to compensate). During Threadfall, it's the male bronze dragon who mated with her who's in charge. The fact that the queens are the only fertile females also means that they're regularly out of action for long periods of time while they tend to their eggs. Supposedly justified in-universe as having the (female) bio-engineer behind the dragons subscribing to traditional gender roles, and building them into her creations as a result.
- Pern itself is a straight-up patriarchy for the most part, but within the Weyr, the Weyrwoman (the queen dragon's rider) is also at the head of an alleged matriarchy: as the queen's rider, she's supposed to be the main player in the Weyr...but only in terms of the domestic, day-to-day running of the place. In fighting—and even in most diplomatic negotiations—she plays second fiddle to the Weyrleader (who got his position because his dragon mated with hers...and he mated with the Weyrwoman as a result. The most successful Weyrwoman usually opt to be The Man Behind the Man instead of claiming full responsibility / credit for their actions.
Intentionally reversed in CJ Cherryh's Chanur Novels. In theory each clan of hani is ruled by a single male who makes all the decisions, but in reality the male is merely a pampered figurehead who rubber-stamps the decisions the females make.
In Nobodys Princess of the Princesses of Myth series a woman is talking to the brothers of Helen of Troy, about how they'll be king someday. When she finds out that in their country the daughter is going to inherit the crown she wants to talk about how the sons will be warriors.

Live-Action TV

The Romulans of Star Trek are often described by Word of God as matriarchal, but in practice this seems to have almost no effect on what we see of them—female Romulan captains are maybe slightly more common than female captains of other villainous species, but most of the Romulans we see captaining ships and holding other positions of authority are still male, and there's no sign that males suffer any kind of discrimination in Romulan society. In contrast, when Star Trek describes a species as patriarchal, it's actually shown to matter—Klingon women are banned from holding seats on their homeworld's High Council, for instance.

Tabletop RPGs

The Drow in Dungeons & Dragons worship a spider goddess and keep men for sex purposes, but Drow women are all gorgeous babes in Chainmail Bikini-like clothes, with Drow men dressing much more conservatively. The most famous Drow, Drizzt Do'Urden, is a male, and it's worth observing that Drow are Exclusively Evil but Drizzt is a Chaotic Good Overused Copycat Character.
Traveller: Played with among Aslan. Male and Female Aslan are roughly equal in status but their domination of separate roles make them a Fantastic Caste System.
The Realm in Exalted is described as a mildly matriarchal society (albeit one where other prejudices matter a lot more than sexism). However, the canonical books have a lot of information about life in the Realm, and there's absolutely no sign that men face any kind of discrimination whatsoever, or that male authority figures are considered even slightly unusual. To all appearances, it's really a strictly gender-egalitarian society that happens to be led by an Empress.

Video Games

The salarians of Mass Effect have strict "matriarchal" gender roles, but in practice this results in all the women being kept on their planet, breeding, while the men are soldiers, commanders and officers and get to go into space. The females supposedly retain all the political power, at least according to the in-game Codex, but it's not until the final game of the trilogy that players actually encounter any sign of this whatsoever (in fact, the whole thing seems to mostly be an excuse to avoid depicting female salarians at all).
Master of Orion II hints at this with the Elerian race. The written text states that the women are the dominant gender, but the only explicitly stated role that men have in Elerian society is in exerting mind control. In addition, most of the Elerian women sprites are scantily-clad technicolor-skinned space babes, so this may overlap with Sexy Matriarchy as well.
The Night Elves of World of Warcraft. On the surface it looks good—but this is a society that divides its genders sharply, with the women making up the military force and worshiping the moon goddess Elune and the men engaging in druidism and worshiping the forest demigod Cenarius, and the society is ruled jointly by the heads of the respective religion. In practice, the high priestess is pretty much a placeholder for her comatose husband, and engaged in a rivalry with her conscious druid counterpart. It is, curiously enough, the druids that go out into the world to help the rest of the Alliance, not the army, and they also get way more credit for their work than the army. Adding insult to injury, game mechanics have the default female dance of the Night Elves be something of a stripper's dance, and the artwork always show them in teeny tiny outfits—even as warriors.
The Qunari of Dragon Age are said to have women hold the political power at home—but not only do we never see them in game, the only leaders actually referred to are men.
The Liontaurs of Quest for Glory III are described as having a social structure that mimics that of real-world lions. Males are believed to be too emotional to make good decisions, so the society is governed by a ruling council of females; while there's a king, he's supposedly a powerless figurehead. In the actual game, though, you spend a lot of time trying to influence the king's opinion and very little on the council, just as if his opinion was the one that actually counted.