I'm not talking about normal questions from an interested questioner, I'm talking about loaded questions and interjections, conveying emotions like concern, or apprehension, or anger.

What does emotional loading mean in practice?

It can come to you in two ways, often both together. 

Emotion conveyed by tone.  For example, imagine an audience member saying, "This is exactly what we did last time." Or  "You mean three times a day?" Tone could make those words neutral, or they could load them with frustration or annoyance.

Emotion conveyed by words. For example, "My team will be annoyed about this."  Or  "The clients are going to be wary."  Or "I'm sceptical about the changes."  The emotional words are annoyed, wary, and sceptical

However the emotion comes at you, you can't help but feel it. The challenge is to respond well. But first...

How not to handle a tough question or interjection

Don't get angry.  If you show anger, annoyance, or even irritation, you've lost the game. You're not coping. You're not in control. The audience decides that you don't care how they feel.  

Don't get defensive.  By all means defend your position, but don't be defensive as you do it. Not clear?  You're defensive if you show anxiety. Once again that says you're not coping.

Don't pretend that you didn't hear the emotion. This is a big one. It's like pretending that part of your audience isn't there. Many managers and executives fall into this trap by responding only to the face value of the words. 

An example:
Interjector:  (tone of frustration), "We've tried that procedure four times already."
Presenter: (fixed pleasant smile) "Actually it was three times. Now, about the scheduile..."

Bad response. The presenter might as well have issued a statement that says, I can't cope with the way you feel. Worse:  if significant numbers of people in the audience also have the same frustration, the speaker's loss of credibility is huge. In fact the biggest emotion in the room may now be: You don't care how we feel, you don't understand where we're coming from. You can't relate to us so we can't relate to you.

Many managers talk themselves into this disastrous thinking: it's better to keep the emotions out of it, stick to the facts, then we can get things done.  Wrong - we do not relate to each other by facts, logic, or rational thought. Emotions are at the centre of what it is to be human. Audiences know that instinctively, and swiftly lose respect for anyone who thinks otherwise.

Pretending not to hear the emotion = instant loss of credibility

Enough on what not to do.  Now, how do we respond to this challenging thing we call emotion?

The right response generates credibility and respect. And it takes courage

Here's the answer, in two parts:

1. For the milder questions and interjections

As you answer, show - with your tone and body language - that you heard the feeling behind the words. That could be raised eyebrows, a slight pause, a nod, more animation, a slightly raised tone.

That shows you heard the feeling behind the words. It's subtle, it's strong, it connects. Audiences crave it in their speakers. Experienced, engaged presenters don't turn this skill on and off for questions and interjections, they never stop doing it.  That's because they are permanently awake to and responding to subtle shifts in the vibes of the room. 

2. When the emotions are strong and obvious

Verbally acknowledge the emotion, then reply.

Build your emotional vocabulary. Be ready to acknowledge emotion in others, using words like, "difficult", "frustrating", "sceptical", "annoying", even "angry".  For example: "Yes, that must be frustrating..."   "Sure. It won't be easy..."   "If I thought that, I would be sceptical too..."  "You have your doubts about this model? [Looks around.] And a few others feel the same way? Okay, I suggest..."  

But isn't that being negative?  If I do that, wouldn't I be undermining my own argument?

Not in the slightest (unless you're looking or sounding anxious).  Acknowledging a negative emotion is not the same as agreeing with the negative argument. It's simply recognising that emotions are a natural part of your presentation, and of any gathering. And you are strong enough to fold them seamlessly and constructively into your presentation.

Accept the feelings, argue the facts. 

In fact you will not positively persuade with your argument until you accept the current negative feelings about it.

Try this example:
Interjector: (angry tones)  "You can't be serious! How the hell are we going to keep up the payments?"
You: (warm, intense, animated)  "Yes! That's the biggest concern for most of us... [looking around] ...agreed?  Well I'm looking at two sources of..."  

I'm saying Yes? To someone who is negative and angry at me?

That's right. The Yes! works because you're welcoming the negative feelings out into the open. You are essentially thanking that person for making the elephant visible. Now you can deal with the real world, which, of course, runs on feelings. This is top rate EQ (emotional intelligence), in a presentation context.

A last thought to ponder.

For top presenters, fully engaged with their audiences, there's no such thing as a negative emotion.