Analysis

This question examines the properties of functions, points that the function passes through, and tests reasoning and computational abilities. It is a basic question.

Given that $f(-x)$ passes through the point $(-1,3)$, we can determine the point through which the graph of $y=f(-x)+1$ must pass.

Solution

Given that the graph of the function $y=f(x)$ passes through the point $(1,3)$,

It follows that $f(-x)$ passes through the point $(-1,3)$,

Therefore, the coordinates of the point that the graph of the function $y=f(-x)+1$ must pass through are $(-1,4)$.

Hence, the answer is $\boxed{(-1,4)}$.