The auto-calculated shipping should be precise or in worst case scenario, very accurate, as we are getting prices from the utilized shipping carriers, - we are using the prices we are getting directly from UPS, FedEx and USPS.
The possible causes of the difference you are talking about may come from incorrect product weight or dimensions in your product settings -> shipping screen.
Additionally, you may have "Delivery Method" set to a particular setting in SETTINGS -> Shipping Carrier. The specified method may not have been available for this order / address.
When a selected delivery method is not available, the next least expensive choice will be made automatically by the system.
You can always check what delivery method was utilized during checkout in your order confirmation email.
Steve - eez.io support