To find the circumference of a circle, we can use the formula:
\[ C = \pi \times d \]
where \( C \) is the circumference and \( d \) is the diameter.
Given that the diameter \( d \) is 4.5 miles and using \( \pi \approx 3.14 \), we can substitute the values into the formula:
\[ C = 3.14 \times 4.5 \]
Now, we calculate:
\[ C = 3.14 \times 4.5 = 14.13 \]
Thus, the estimated circumference of the circle is:
\[ \boxed{14.13} \text{ miles} \]