This calculation method can produce more accurate estimation. Using the more accurate estimation will lead to a more accurate final result.
Although I know that there is a special sentence structure "the more/er... the more/er", I am not sure that it is possible to add "the" to "more" in normal sentences such as the above sentence I created.
You must note that the definite article is not used together with "more", but together with "estimation. "More" (in both sentences) is used together with "accurate" for creating the comparative.
Also, it is important to note that the sentence requires an article, either definite (the) or indefinite (a).
Using a more accurate estimation will lead to a more accurate final result.
NOTE: the first sentence is missing an indefinite article:
This calculation method can produce a more accurate estimation.
Although not mandatory, the two sentences can be merged into a single one (considering that they share a big amount of words):
This calculation method can produce a more accurate estimation, which in turn will lead to a more accurate final result.
The definite article "the" is used when the reader should know which instance of that object you are talking about. In your example, the object is an estimation --- specifically, the "more accurate estimation" described in the previous sentence. In this case, "the more" only works in the second sentence because the object is introduced in the first sentence.
"The" is not added only to "more" in your example. It's added to the whole noun phrase: "the more accurate estimation".
Here's a similar sentence that avoids the word "more" completely but uses "the":
This calculation method produces accurate results. The results it produces can be used in variety of applications
In this case, it's "the results," which is equivalent to "the more accurate estimation" in your example
"The" can also be used when something is countable or measurable (that reference has good examples of when a certain noun is countable or not).
"More" can mean "an amount larger than expected" or "an amount larger than before" (see the definition in Macmillan dictionary), so while it may not refer to a specific number, it can refer to something measurable.
The more I talk to you, the more I like you!
She didn't know what to do on a plane her first time, but the more she traveled, the more she learned
