Migraine meditation mantras provide you with a technique to help reduce the severity and duration of your migraines. Science backs this up.
The repetition is said to calm the autonomic nervous system and induce sleep so we can better cope with and endure our attacks.
With some techniques, you must agree to secrecy if you are to be gifted with one of the mantras, unique to you and only you.
Your mantra is considered holy, blessed, sacred and precious. In fact, it is top secret.
I kept mine top secret, well, I still do. I believed it was sacred and unique to me, until I researched for this article.
I don't want to divulge secret information, nor do I want to spoil any profound shifts, which certain techniques have the ability to do.
So please read on, with caution.
A mantra is a sound, or vibration, that emanates and is repeated. It is rarely a familiar English word, but it may hold meaning. It is that simple. According to meditation is easy.com, a mantra is basically any sound that is repetitious like the sound of the wind blowing through trees, or our footsteps on the earth. Our heart beat and our breathing is also considered to be a mantra.
"Sound has enormous power, in fact it has the power to create an entire universe. It is written that God originally manifested as sound. In the beginning was the Word, and the Word was with God, and the Word was God." (New Testament, John 1:1-2 cited in meditationiseasy.com)
Mantras exist in many rituals. Most famous is Om. The ancient Indian sages believed that this sound and its vibration echoed infinitely all the way through the universe.
The recent work of Masaru Emoto (1943 – present) on the effect of words on water crystals using the Magnetic Resonance Analysis technology for the concept of micro cluster water in the US is starting to explain this phenomenon.
So the migraine meditation mantras you can choose, in my own translation, are really meaningless sounds that distract the mind and cause insignificant or no thoughts, a clear mind.
Rigpa.org's Feb. 20th newsletter had this to say on mantras. I thought it was just beautiful definition, much better than anything I could explain:
A meditation technique used a great deal in Tibetan Buddhism is uniting the mind with the sound of a mantra. The definition of mantra is "that which protects the mind." That which protects the mind from negativity, or which protects you from your own mind, is mantra.
When you are nervous, disoriented, or emotionally fragile, inspired chanting or reciting of a mantra can change the state of your mind completely, by transforming its energy and atmosphere.
How is this possible?
Mantra is the essence of sound, the embodiment of the truth in the form of sound. Each syllable is impregnated with spiritual power, condenses a deep spiritual truth, and vibrates with the blessing of the speech of the Buddhas.
It is also said that the mind rides on the subtle energy of the breath, the prana, which moves through and purifies the subtle channels of the body. So when you chant a mantra, you are charging your breath and energy with the energy of the mantra, and so working directly on your mind and your subtle body.
So you see, by using migraine meditation mantras, you can change your energy.
Using migraine meditation mantras provides the technique of a simple mental repetition of a meaningless mantra or meaningless word twice every 15 seconds, with a 15 second pause in between, for 15 to 20 minutes.
There are seven levels of advanced technique mantras that have lovely meanings.
SHRI means "Oh most beautiful";
AING is the name of the "Hindu goddess Saraswati";
and NAMAH means "I bow down." 
Here are the advanced techniques, as listed at minet.org, and my translations:
First: AING NAMAH – I bow down before the goddess Saraswati
Second: SHRI AING NAMAH – Oh most beautiful goddess Saraswati, I bow down
Third: SHRI AING NAMAH NAMAH – I bow down twice before the beautiful goddess Saraswati
Fourth: SHRI SHRI (your mantra once) NAMAH NAMAH
Fifth: SHRI SHRI (your mantra twice) NAMAH NAMAH
Sixth: SHRI SHRI (your mantra twice) NAMAH NAMAH
(Attention and awareness to be held in the heart area)
Seventh: This level reaches the "Age of Enlightenment Technique" which is a "system of putting attention on parts of the body, environment, world and outer space."
Ayurveda uses, what they consider a primordial sound - "AMRITA," as a mantra. Many hold attention in the heart area.
Tibetans recite this mantra quietly or loudly in an inspiring way and then rest in the silence that follows –
“OM AH HUM VAJRA GURU PADMA SIDDHI HUM" or
"OM AH HUNG BENZA GURU PEMA SIDDHI HUNG.”
This is the mantra of Padmasambhava, the mantra of all the Buddha’s and masters. It is said to be “uniquely powerful for peace, for healing, for transformation, and for protection against the violence” in our current culture. 
Those touch my heart a little more than the other repetitive meditation mantras. But it is important to experiment and discover what works for you.
Some ideas I have for migraine meditation mantras are: "I am pain free", however many techniques say not to use the word pain!
Another good one is "freedom" or "space". You can just let your neck and shoulders relax as you repeat it. You can also use the word "relax".
I highly recommending learning to meditate and do yourself the favor by reducing stress and worries. And hopefully any further migraine attacks.
Here's a link to my course, to help you get started on this path...
Migraine Meditation Mantras References:
1. Meditation Information Network (2012). Supporting critical examination of Transcendental Meditation® (The TM® Program) and the programs associated with Maharishi Mahesh Yogi. Available [online] at: http://minet.org/. Updated Dec. 2, 2018
2. OWN, Oprah Winfrey (May 6th, 2012) [Online], Available at: http://www.oprah.com/own-super-soul-sunday/Thich-Nhat-Hanhs-Four-Mantras-Video
3. RIGPA (2009) Sogyal Rinpoche teaches the authentic Buddhist tradition of Tibet. [Online], Available at: http://www.rigpa.org/