Remember the film Dog Day Afternoon? Al Pacino at his best.
I have a feeling hostage negotiating involves making a personal connection with the hostage taker and humanising the hostages in their eyes. Keeping the dialogue open is important. So is gaining the hostage taker's trust. A good, soft, sales technique might help, like open ended questions to force a dialogue as opposed to yes and no, etc. If you get to know who they are, how they tick, and what they want it might be easier. The trick might be to give the hostage takers the illusion of control then making them think releasing the victims was their idea and in their favour. They want something. The negotiator has to find the compromise which fits with their need yet gets the hostages out. But I don't really know.
I'm sure if you google 'the life if a hostage negotiator' or hostage negotiation tactics, you'll find tons.
There's a documentary about a US hostage negotiator who helped release military personnel captivated during combat. Irak, I think. The hostage takers demanded he'd go with them to see their boss to make a deal. The negotiator was blindfolded and loaded in the back of a car then taken somewhere to do business. It was interesting to hear his recollection about being at their mercy with no life line to the US military. After he struck a deal with the boss, he was then sent back to the base so he could make good in their deal. Depending who your protagonist is here might be something in there you can use.
You might get info by looking at old news stories. There was a hotage situation at the Lybian embassy in London, I think in the 60s or 70s, I can't remember. Negotiations failed and the SAS went in and saved the day. I watched a documentary and have a vague memory that the hostages didn't run to savety at the end, but were held by security forces for ID checks to make sure none of the hostage takers were posing as victims in order to get out home free. I'm fairly sure 'ID ckecks' like that are common practice to make sure they get all the bad guys. Might be something to explore.
There was also a hostage situation in Russia that didn't end well. In the 90s, I think. If I remember right, the authorities tried to pump 'sleeping' gas into the cinema but killed hostages that way. Something like that.
And don't forget the stockholm syndrome.
Also, some hostage takers might never ever have the intention of releasing their victims. For them the situation serves to promote their cause as can be seen in some of the beheadings happening by terrorist organistations in the midle east. You might want to bear that in mind when you write your antagonists / hostage takers. Get their motivation clear. Does their motivation allow for negotiation. By taking hostages they are inviting a dialogue in a sense depending on what it is they want and their end goal. Guys like ISIS probably don't care about negotiations. They' are kidnapping and executing for an effect. They're gaining by killing.