Estimation, estimate both mean the act of valuing or appraising, but they are rarely interchangeable.
In general, estimation implies the manner or measure in which a person or thing is valued or esteemed. Often the term comes close to personal opinion or point of view, especially in respect to a thing’s value.
In general, estimate applies to the result of an appraisal or an evaluation (as of a thing’s worth, its cost, its size, or its prospects). It may connote an approximation to the truth that has been reached either by guessing or conjecture or as the outcome of careful consideration, expert knowledge, or profound study.
In a technical sense estimate implies the sum for which a piece of work (as the erection or repair of a building) can or will be undertaken.