Hello and thanks for researching this very important question!
Parkinson's Disease in humans causes, among other things, a progressive muscle tremor when the body is at rest...an important distinction from other neuromuscular illnesses that produce muscle tremor when the affected limb/part is moving!
While there is not an actual Parkinsons-condition identified in cats, there are a lot of conditions in older felines that can cause a muscle tremor.
1) Excitement is mediated through the brain by chemicals such as serotonin and norepinephrine. It may be that your cat's system is either giving out too much excitatory chemicals, or she is especially sensitive to their presence. Very prolonged "firing" of nerves in the muscles can cause discomfort. Excited shivering can be considered normal in the absence of other symptoms of illness, and is ordinarily seen throughout a pet's lifetime.
2) Pain in the joints associated with injury, arthritis or other degenerative diseases can cause the excitatory system to become over-active, due to the body's response to stress.
3) Tumors growing in the brain and/or spinal cord can press on nerves that control muscle movement. Other structural problems, such as severe arthritis or disc degeneration can cause severe nerve compression as well. These compressions can become serious enough to cause paralysis of one or more limbs.
4) Degenerative conditions in the nerves and muscles themselves are often to blame in older cats: these conditions are accompanied by reduction of muscle mass in the affected body part(s)...check your pet for thinness and boniness over the head and along the length of the legs. This often occurs slowly over time and can be missed.
5) Disease in other organs in the body can lead to build up of metabolic toxins in the blood. These by-products can reach the brain and cause dysfunction.
6) Occasionally, we still do not know what causes these symptoms in older pets ("Idiopathic Tremor")...in this way, there is similarity to Parkinson's only in that more research is needed over time to find the root cause(s).
***To get a full picture of what has been happening to your dear pet, she would need to be evaluated by your regular vet, to make sure there is nothing obvious going on. The next step after that would be a visit to a Veterinary Neurologist. Your regular vet can provide you with a reliable referral in your area, or you can use this link to locate someone yourself: