Cardinals are super parents. If the baby is up off it's hocks, (basically means he stands up and hops around) then he is a fledgling and not a nestling.
His parents will continue to look for him for several days. Both male and female cardinals feed their young and this includes those babies who have fledged. Actually other cardinals may help also as they can be very communal during this time of year.
It is easy to make an alternative nest. One way is to take a milk jug and cut it in half. Punch several holes in the bottom so if it rains, the bird wont drown.
Add something in the way of soft straw (grass is cold, straw is better) and nail the milk jug as high up a tree as you can reach.
Watch from a distance to see if the parents tend to him. I have little doubt they will, from what your saying.
If he is a fledgling, then he will more than likely will jump out of the nest, as it should be. When birds first fledge they are often very unsure and clumsy. Much like a child starting to move about on his own. They gather quickness very fast and become mobile.
Cardinals fledge quickly and have a high protein and calcium requirement while young. If your forced to help in this situation, call your Department of Natural Resources (DNR) and see if there is a Rehabber in your area.
In the meanwhile, dried catfood can be used. Soak the pellets until they are soft and mushy, then offer to him. Of course cut them down to size if need be. They eat very often. Primarily during the day, that is what the parent do... they go back and forth feeding their young, with the peak times in the early day and early evening. They do not feed their young at night as they have roosted in for the night.
If you have a dog you can use dry dog food instead. Cat food is just normally higher in protein than dog and also canned foods. Kitten dry food is good. Just remember to soak it first..
Watch for temperature. A bird's temperature is much higher than ours and if they chill, you have a problem.
Good luck.