To find the unit cost per pizza, we can divide the total cost of the order by the number of pizzas.
The total cost of the order is $58.50, and Mr. Emery bought 6 pizzas. The calculation will be as follows:
\[ \text{Unit cost per pizza} = \frac{\text{Total cost}}{\text{Number of pizzas}} = \frac{58.50}{6} \]
Now, we perform the division:
\[ \frac{58.50}{6} = 9.75 \]
Therefore, the unit cost per pizza is \( \boxed{9.75} \).