When I have shipped in the past, I've used the UPS website to get a rough idea of how much it might cost.
1 - Go to http://www.ups.com/
2 - On the left menu, click "Calculate time and cost"
3 - Enter the estimated weight of the package and the zip codes of where the milk will be shipped from, and shipped to. You will be given multiple shipping options and price quotes for everything from ground shipping to overnight.
To find out how long ground shipping will take, there is a line in the box that says "Days In Transit:". Depending on how far the milk will be traveling, ground shipping could take as little as 1-2 days, and is therefore extremely economical.
Estimating Shipping Weight
1 fl oz of breastmilk weighs just about an ounce, so it's safe to assume that 160oz of frozen milk will be about 10lbs in weight - plus the weight of the cooler. With that information, you can make a general estimate of how much the whole shipment will weigh.
For example, one of the most recent shipments of milk that came for my son was about 1100oz. The weight of the package was 75lbs. 1100oz divided by 16 is 68.75 lbs, so the cooler was probably in the neighborhood of 6 lbs.
*** I will be weighing some of my coolers in the next couple of days to give you an idea of how much they weigh - bear with me!***