With the future implementation of RingCT, transaction amounts will be hidden.
How will a miner determine if a RingCT transaction includes a sufficient enough transaction fee to be included in a block?
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Jwinterm's answer is more an answer to this question, which asked how transaction fees will be calculated after Ring CT. The answer to your question can be found in the Ring CT whitepaper. More specifically in section 4.3, which states:
As Monero is strongly decentralized (i.e. proof of work) it is necessary to pay miners a transaction fee for each transaction. This helps with the network security to prevent blockchain bloat. These fees must be paid "unmasked", i.e., just as bH, rather than xG + bH, and for some standardized amount b so that the miner can verify that b · H = bH and thus there is enough money for the transaction fee while still having the equations in terms of H so the necessary relations of section 4 hold.
Fees are based on the size of the transaction in bytes, not the size in Monero. I believe that ring CT will slightly increase the average size of transactions, so fees will be slightly increase unless other changes are made (such as fee per kB), but the size of the transaction fee has nothing or little to do with the amount of XMR you're sending.