This. Not least because you sure do not want to find it somehow disappeared from checked baggage while out of your view....you will always want to be 100% sure of where it is.

But also because if you do get selected for secondary screening they do not check your pockets except in extremely suspicious situations at which point you can claim you were so nervous about the process you forgot it was in your pocket and you want to declare it now. Then you would produce a receipt to establish value. but do not worry about it, the duty will be relatively minor amount unless you are planning to give your intended a VERY expensive pebble. In which case, you probably already have the means to pay the duty.

Having said all of that - a ballpark number for planning purposes: only the value above US$500 would be dutiable and while it is difficult to find reliable information, this page with a 2017 date, Customs or Import duty for Diamond jewellery - pendants,rings,necklaces,ear-rings,gold coins to Mexico (customsdutyfree.com) also has a calculator that indicates only VAT of 6% would be due - so a little less than $600 on a $10,000 ring.

the most reliable thing to do is contact your nearest Mexican consulate/embassy and ask them. Or, you can try to find a friendly customs broker who deals with Mexico who can give you an accurate number.