I run skill checks this way in my PnP games:
1) I, the DM, call for skill checks, not you, the player
2) I'll call for a skill check when it's needed
3) Tell me what you want to do, rather than telling me 'I want to make a stealth check'
Hopefully this encourages my players to role-play first, and roll dice last.
What I see in most games these days is a skill check first, role-play last, approach. For example, if there's a Science check, it'll say [SCIENCE], and the player knows they can pick this if they have the science skill and it'll be a positive thing that will most likely solve the encounter. They don't even have to look at the dialogue, or the thing that the character is going to do. If there's any role-playing at all, it's secondary, because the player is primarily looking for that [SCIENCE] tag, and the actual dialogue is a secondary concern, if it's a concern at all.
Whereas what should happen is that players have a choice of actions or dialogues, and by following one that appeals to them, or picking intelligently, they might arrive at a skill check, which they can back out from and seek another approach if they wish.
For example, let's say you want to persuade an NPC to fuck you. A role-playing approach is to attempt to say the right thing to the NPC, based on what you know about them, or what you can find out through exploration or conversation. At the end of a successfully-navigated dialogue sequence where the player says the right thing, there's a check of some sort. Like, ok you said all the right words, now are you actually charming or buff enough for her to go 'ok let's fuck', or is she going to let you down lightly.
Whereas the braindead approach most games take nowadays is a simple yes/no binary check right at the start of conversations or encounters, which you either succeed or fail purely based on mechanics, there's no role-playing at all.
A good example of this can be seen in Fallout: New Vegas' final encounter with Legate Lanius, where you actually have to pick the right conversation choices and then spaced throughout the dialogue are actual Speech checks, but you still have to actually THINK about what you're saying, you can't mindlessly click through the dialogue.