I will start with kidney problems, often seen in older cats, so I will start with cats -
Often these cats are inappetant as they don't feel well, and getting them to eat anything is a challenge.
Many of the cats I see have been put on a commercial "kidney diet" which is unpalatable and they are just not eating.
The important thing is that the quality of the protein is high (meaning it is easy to digest) so animal source protein is much better for these cats than a grain or vegetable source protein. So, take them off all commercial dry food. Fluid intake is very important for these cats, so fresh raw food is best.
I have attached a paper which looks at "the mythology of protein restriction" which emphasises the fact that cats are obligate carnivores and need a high protein diet at all times, even when their kidneys are failing. http://www.4dik.net/folder-pdf/low-protein-diet-pdf.php
The protein source should be species appropriate, so I recommend feeding chicken, rabbit, quail, oily fish, easily digested proteins.
The importance of reducing the phosphate level in a renal diet has been recognised for many years and I use a nutritional supplement called "Ipakitine" which is a combination of calcium carbonate (a proven phosphate binder) and "chitosan" which acts as an absorbent in the intestines, lowering the absorption of phosphates and ureamic toxins. This can be sprinkled on the food.
Kidney problems in dogs are less common but the same principles apply -
Raw food, high quality source of protein that is species specific and easily digested, and a phosphate binding supplement. Again, I would be offering chicken, fish, rabbit, quail, all easy to digest.
I would offer all of these in big pieces of raw meaty bones, with organs attached where possible. I try not to list percentages of meat to bone to organs to green tripe. Most dogs with a decreased appetite love green tripe so it sometimes makes up to 30% of the diet to get them eating. We feed organ meats attached to our frames or carcasses, but if adding them in I would be looking at 5-10%.
I will answer further questions this afternoon.