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You can go to usps.com and get price quotes from them for most anything, if you want to use the regular post office. http://ircalc.usps.gov/ Beware that you will have to fill out additional paperwork for shipping an item to another country - even Canada.

Shipping a Mouthpiece from the US to the UK will range from about $12 to about $25 based on what postal service you select and what type packing you use.

Suprisingly using global priority with the free box they provide is one of the best deals at about $15 as it gets there in about 4-6 days.

Sending airmail parcel post with your own box takes 4-10 days but costs MORE at around $22 and the slowest method.. surface parcel post takes 4-6 weeks yet costs the MOST at around $25

If you pack in a smaller type box you might be able to fit in the air letter post rates which will save you a good bit though. It still is going to be in the $12 range and will take about a week to get there.

Do not skimp on packing material especially around the shank end. If you can feel the mouthpiece move when you shake the box hard.. you DO NOT have it packed well enough for international shipping.

You will need to fill out a customs form at the post office as well.

Good Luck