How do you give emotional support?

As an SO who is in a relationship with a man (a PA) who struggles with this, all I can say is to practice empathy.
Practice looking at strangers, trying to imagine what sort of emotions they are feeling. People-watching is what I like to call this.
Try to empathize with your wife's emotions instead of going immediately to "fix it" mode. She just needs to sit with her emotions for a while sometimes.
Hugging her and telling her it's going to be okay is good, though. Even if you don't feel like it supports much, it probably does more than you know.

Sometimes emotional support can mean just listening when she needs to get something off her chest. My fiance and I are working on that part together. He never listened, he only tried to fix it. So, if you just stroke her back while she talks or cries, she will feel more supported than you just sitting there staring blankly at her or offering solutions that she's not ready for.

Here is a site I just found that has a couple of exercises you can try. I think number 2 says it all.

 

Integrity, transparency and consistency

 

Integrity - do what you say you will do.. Don't be a flake, don't forget and don't make excuses.
Be a man of your word.
Transparency - at whatever level she needs.
Be open, be honest and don't rush to anger.
Be consistent - in everything that you do.
She needs to be able to depend on your actions.
Without consistency she will continue to backslide with her healing.
No trust can be established and it can be detrimental to your SO to be constantly reset because she feels the lack of trust.

Just my two cents.

 

As was pointed out this is a common male/female dynamic. A woman just sometimes wants to talk, she’s not looking for you to solve a problem, just to listen. Another problem I see with addicts is that many are not in touch with their own feelings. Men in general are socialized to not express feelings other than anger. And addicts push all their feelings down. It’s really hard to empathize when you either never felt that way yourself or if you did not know it. So you can see she’s hurting and that hurts you but still struggle to understand. It also may help to get more in touch with your own feelings. My ex was a PMO addict and he really struggled with this. I read a book that recommended that the person struggling with this try to name their own feelings when they arise.

But honestly what @Kenzi said is exactly on point for what you can do to support her. What I said can help, but she’s spot on. And ask her what she needs and do it. Good luck!

 

You are off to a good start: listening and hugging her. I found the brain fog from P abuse to definitely cause myself to not be empathetic, to look for a quick fix, and just not be present. It is near impossible to be emotional support for someone through text message or email. They are just characters on a screen. Even if you are an eloquent writer, phrases can be misunderstood, the depth of their meaning lost, the nuances of tone and inflection from a real conversation just can’t be there.
You can certainly say via text that “i’m Sorry you feel <the way you interpret her feelings>, I love you and would like to talk to you more about this when I get home.” Acknowledgement and understanding is important for that emotional support. Feeling and relating to what she is going through also helps. Try to identify with what she is going through, perhaps you can talk about a similar feeling or experience that she might relate with. It’s okay to ask her if she needs anything from you, if you don’t know what to do or how to respond. Let her know you will embrace it, you’ll listen, that you can relate and be vulnerable with her.
The damaged caused to your relationship through your PMO abuse can seem like a push and pull game with her, much like some days urges or triggers are non existent and other days you it could be overwhelming for a PA. She going through similar struggles, sometimes the feeling or depth of the abuse or neglect is too much to deal with, and negativity sets in, other times she can recognize the level of effort you are putting into recovery. You may also find value in familiarizing yourself with the greif cycle to better give yourself an understanding of what she is going through. When she pushes, don’t get defensive, don’t stonewall. When she pulls don’t hesitate to bring her in and share your love with her.
If it any time it all gets overwhelming, or starts turning into a conflict it is safe to call for a break and come back to the conversation. It’s what they call flooding, and it can lead us to saying rash things and fighting, so taking a break to gather thoughts and emotions is necessary, rather than living In the moment.

Let your guard down and let her see who you really are. Keep listening. Keep giving positive and healing touches to let her know she isn’t alone in all this and that you are there for her.

 

Saying, "it'll be all right" is a little patronising - how do you know?
Brené Brown is really good at offering advice for this:

 

This is ridiculously spot on. The amount of times I’ve heard in an argument not to say I’m going to do something and then not do it...even if it’s an honest mistake. I have to learn to not say I’m going to do something unless there is absolutely NO doubt that it will be done.
Consistency...it’s like being reliable and trust worthy. When you constantly do the things you are supposed to do, when you continue to try and don’t slack on duties, you show that you are someone who can be trusted. Not in terms of lying and honesty (though that should be the number one thing you are being sure to correct) but you can be trusted as a form of security in the relationship.
Transparency goes along with honesty. Don’t hide what you are feeling. Don’t keep secrets. Be open and always act as though your partner is watching you. That’s the part I forget sometimes. Stopping and thinking “if she saw me right now, what would she think?”

I know these examples are more for the relationship at whole, and not exactly during a moment of support. But these are so incredibly important. If you do these things, and just listen. Don’t try to solve the issue. Just listen and agree if what she’s saying is true. You may want to offer a plan of some kind to work with for the time being. But know issues can’t be fixed all the time RIGHT at that moment.