Back when Charles Poloquin was still writing for T-mag he wrote of a means of exercising your neck. I’ll do my best to describe it and save you the search. Stand straight up against a wall and press the back of your head hard up against it. Then walk forward so that your body is at an approx 45’ angle from the wall. The idea is just to be supporting your bodyweight with only two points of contact. The back of your head against the wall and your heels. Hold this position for as long as you are able. And believe me, when you first start off it won’t be long. Take a rest and do a few more sets like this. Once you can hold this contraction for a couple of mins, you can move on to a swiss ball. Similar exercise. Only difference is now you use the ball like a big pillow, with just the back of your head resting on it and your heels on the floor. In this position you can incorporate small movements. Allowing you chin to come down to your chest, before flexing your neck muscles to so that the line of your spine is once more straight from the base right to the skull. And for the pedantic few out there, yes I know the spine is not straight. After this you can incorporate extra resistance by holding a weight plate on your chest.
There you have it. A safe way to build up your neck. Though I have to admit, lifting with free weights in my garage as I do. I am not familiar with neck machines you are talking about.
One final bit of info. When you do this exercise, be prepared for dizzy head spins that will last a few seconds when you immediately stand straight again after finishing a set.