Being a layman, you can only give advice to the students. When their test anxiety is serious, the best advice you can give them is - seek professional help.
There are, as you say, numerous ways to relieve 'normal' anxiety. A good web source is WebMD, that gives the following tips, which may aid your students too:
- Learn your students to study efficiently; your institution may offer dedicated study-skill courses to the students;
- You can learn them test-taking strategies;
- Students feel more relaxed if they study systematically and practice the material that will be on a test. Establish a consistent pretest routine. That way they'll learn what works best for them, which eases stress levels;
- Teach them relaxation techniques. There are a multitude of them, applicable to either right before the test, or during the test to help them stay calm, e.g., breathing techniques, muscle relaxing strategies, closing the eyes and imagining a positive outcome, or meditation techniques;
- Remind them to eat and drink. Their brain needs fuel to function. They should eat a meal before the test and drink plenty of water. However, sugary drinks such as soda pops can cause the blood sugar to peak and then steeply drop. Also, caffeine may not be wise as it can increase anxiety;
- Let them exercise. Regular aerobic exercise, and exercising on exam day, can release tension;
- Urge them to get plenty of sleep. Sleep is directly related to academic performance. Preteens and teenagers especially need to get regular, solid sleep;
- Make sure your students can openly discuss anxiety issues with you;
- A student may have a learning disability that requires professional help. Test anxiety may improve by addressing the underlying condition that interferes with the ability to learn, focus or concentrate — for example, attention-deficit/hyperactivity disorder (ADHD) or dyslexia. If a student has been diagnosed with a learning disability you can provide them with assistance with test taking, such as extra time to complete a test or having questions read aloud;
- And again - urge them to seek professional help, if necessary. Talk therapy (psychotherapy) with a psychologist or other mental health provider can help them to work through their feelings, thoughts and behaviors that may cause or worsen anxiety. You can ask around at your institution if it has a counseling service in-house, otherwise you can advise your students to seek professional help outside the school's setting.