mid-15c., from Old French estimer "to estimate, determine" (14c.), from Latin aestimare "to value, determine the value of, appraise," perhaps ultimately from *ais-temos "one who cuts copper," i.e. mints money (but de Vaan finds this "not very credible"). At first used as we would now use estimate; sense of "value, respect" is 1530s. Related: Esteemed; esteeming.

1902, a blending of guess (v.) and estimate (v.). Related: Guesstimated; guesstimating. As a noun from 1906.

"estimate erroneously," 1778, from mis- (1) "badly, wrongly" + estimate (v.). Related: Misestimated; misestimating. As a noun by 1843 (misestimation is by 1809).

also over-estimate, "estimate too highly, overvalue," 1768, from over- + estimate (v.). Related: Over-estimated; over-estimating.

also under-estimate, 1812, "to estimate at too low an amount," from under + estimate (v.). The meaning "to rank too low, undervalue" is recorded from 1850. As a noun, "a too-low estimate," by 1882. Related: Underestimated; underestimating; underestimation (1853).