Also, if it's good, it'll have a Bessel or x dB Gaussian shape.
Bad old Teks (from the TDS2xx and other families I think??) just kind of did whatever, often peaking their response, presumably to hit risetime targets, and.. not much else?
Classic Teks, from the tube days, using distributed amplifiers, I think had extremely sharp cutoffs -- each stage was designed for a reasonably soft Bessel profile, but all together, plus the lumped-equivalent delay line, made for an aggressive asymptote -- on the upside, the Tek 585 gave you a flat 85MHz+ of bandwidth, in an almost/all vacuum tube design, back in 1959!
A more reasonable example from their mid age lines, my TDS460 -- the analog front end seems to be well behaved, dropping off gradually beyond the rated 350MHz. Lots of custom (or at least specialized) ceramic+gold chips in there, the front end and ADCs. I've observed signals (with stable trigger) over 650MHz with it. (Main downside: the equivalent time sampling is preposterously slow on the lowest time/div settings. Modern scopes are almost exclusively real-time, and this isn't a problem.)
Tim