I have walked onto concert platforms for most of my life and I still know exactly the sensation an adult beginner describes when their partner comes into the room. It does not go away with experience. What changes is what you do with it, and that part is learnable.
First, what is actually going wrong, because the usual explanation — nerves — is too vague to act on.
The piece was never as secure as it felt
This is the largest single cause and the least welcome.
Playing alone, you are running on a chain of physical habit: each movement cues the next. It is smooth and it feels like knowing the piece. It is not the same as knowing the piece. Break the chain anywhere — and attention on you is precisely what breaks it — and there is nothing underneath to fall back on, because you never needed anything underneath.
The test: start from the middle. Open the music at bar seventeen and begin there. If you cannot, you have a chain rather than a piece, and that is what collapses in company. The fix is to practice starting from four or five different points, so that a break drops you onto solid ground instead of into nothing.
You are listening to yourself differently
Alone, you listen to the music. With someone there, you listen to yourself being heard — monitoring, judging, predicting their reaction. That is a second task running alongside the playing, and it takes capacity from exactly the place the playing needs it.
The only thing I have found that genuinely helps is giving your attention a specific job it cannot do while it is monitoring. Not “relax” — that is not a task. Something concrete: make the left hand quieter than the right in this section. Listen for the last note of each phrase. Attention will go somewhere; decide where.
The tempo runs away
Almost everyone plays faster in front of people, without noticing, and the faster tempo is what causes the mistakes that are then blamed on nerves.
Set the first phrase deliberately slower than feels right. You will not sound slow; you will sound composed. The rate at which you play the opening bar effectively decides the rest.
The breathing stops
Watch yourself at the difficult bar and you will find you are holding your breath. A held breath stiffens the shoulders, a stiff shoulder cannot deliver weight, and a hand that cannot get weight from the arm compensates by gripping. That whole chain starts with the breath.
Mark two or three places in the score where you will exhale — actually mark them, in pencil — and practice breathing there until it is as automatic as the fingering. This is the oldest trick in the profession and the most reliable.
What to do in the week before
Play it once a day at the wrong time. Cold, first thing, without a warm-up, without a run-through. Performance is a cold start and practicing only warm is practicing the wrong conditions.
Record yourself. A running camera produces a surprising amount of the same self-consciousness, and it is the cheapest rehearsal for it available.
Play it for one safe person. One is the step. The gap between nobody and one person is far larger than the gap between one and twenty.
Decide in advance what you do when you stumble. This is the part people skip. If you have no plan, you will stop and apologize. If you have decided — carry on from the next phrase, no comment, no expression — you will do that instead, and the listener will very often not have noticed anything.
The thing nobody tells beginners
The people listening to you are not assessing you. They cannot hear the wrong note in bar twelve; they hear whether the music went somewhere. A performance with three errors and a shape is a good performance. A flawless one with no direction is not, and every musician knows it.
That is not consolation. It is the actual standard, and playing to it rather than to an imagined error count is what eventually makes playing for people enjoyable.
If you would like to practice being heard by one person who is not going to be startled by anything, send me a recording. Feedback is free while the pilot runs, and this is a reasonable and quite common reason to use it.