There's lots of literature, advice, and hearsay out there on muscle strength, flexibility, etc., Comparatively little is available for the tendons in regards to martial arts.
Knowing more about their importance and special characteristics, as well as any precautions would be helpful.
For example: Intuitively, having strong muscles but weak tendons seems like a more dangerous situation to be in than vice versa, since tendons take longer to heal when damaged. Is that in fact the case?
Tendons are a 3d lattice structure, and generally fairly strong. They are strengthened in the same way that muscles are, however where a muscle will recover in 24-48 hours from a training session, tendons take 48-72 hours.
There is a good breakdown here with some referenced studies on how to make them stronger with supplementation and training.
As far as flexibility, the greater danger in having inflexible muscles in regards to tendons, is the stretch reflex. Each tendon has one (think of when the doctor whacks your knee with a hammer, that twitch is the tendon reflex), and when the tendon is suddenly stretched it causes the muscle to tighten momentarily as a protection mechanism. If you are in the middle of a kick and that happens, you can possibly tear the muscle or the tendon. That's basically what flexibility training is, not so much training the muscle but training the mind to accept greater stretch before the receptors in the muscle say "enough". (An unconscious person can be stretched way beyond their normal limits when awake).
Ligaments anchor bone to bone, and they are not intended to stretch. If you remember the old click pens with springs in them, if you stretch out the spring it doesn't go back. Same with ligaments, so if you stretch a ligament it stays stretched, hence some shoulder ligaments basically get a "tuck" to help alleviate chronic separated shoulders.
Tendons anchor muscle to bone, and the three main injuries due to tendon issues are torn muscles, ruptured tendons, or avulsion fractures (Where the tendon tears away a piece of bone).
Regular resistance training, sleep/recovery, nutrition and hydration are your best bets. As shown in the study, there are some advantages to supplementation. You may also benefit from flexibility or yoga training, depending on your current level.
