How to prove two methods are “similar”?

We are testing two imaging machines. One of the machines has been validated numerous times. However, we built the new machine and we need to prove that it is similar/comparable to the validated machine.

So, the machines image a certain tube and determine a physical property. With several image loops, we can find the same physical property, with slight variations, and obtain a standard deviation for the physical property for each machine.

We want to prove the similarity of the new method to the old method.

I have basic understanding of statistics. I tried to solve this by showing a large P value, just to realize that it is not sufficient proof. (P value can only prove rejection of similarity).

Can we publish an article if we say that the two methods give the same order of magnitude results? Is this possible or do we need a clear statistical proof?