The outline of the Little Dipper, like the Big Dipper, is formed by seven stars. Polaris (m = 2.02) marks the end of the handle. The next star in, going towards the cup, is delta UMi (m = 4.36). This is followed by epsilon UMi (m = 4.23). At the top of the cup zeta UMi (m= 4.32) is the star closest to Polaris. Kochab (m = 2.08) marks the other side of the top. At the bottom of the cup, eta UMi (m = 4.95) is the star closest to Polaris. Pherkad (m = 3.05) marks the other side of the bottom.
If you can only see two stars (Polaris and Kochab), your limiting magnitude is about 2.5 or so. If you can see these two plus Pherkad, your limiting magnitude is about 3.5 or so. If you can see all but eta UMi, your limiting magnitude is around 4.5 or so. If you can see all seven, your limiting magnitude is better that about 5.5 or so.
Note that this technique only gives you an estimate of the limiting magnitude in the direction of the Little Dipper. It can be significantly different in other directions.