When a piece of meat is in a mixture that should nullify it, we don't consider it nullified if it is ראוי להתכבד, or "worthy of being honored", something you would serve to a guest. Is there some kind of objective measure for this, or is it dependent on the time and place, or even the dish or the guest?
It is subject to current societal standards.
Aruch HaShulchan (YD 101:21):
כבר נתבאר דחה"ל תלוי לפי המקום ולפי הזמן והכל לפי ראות עיני המורה
It has already been explained that chaticha hare'uya lehischabed depends on the place and the time, and it all goes according to the way it appears before the [particular] rabbi.
An important aside, the piece can only be a חה"ל if by itself it is ראויה להתכבד. If it's a small piece of meat that is only ראויה להתכבד when served with more pieces of meat, it is disqualified. (AhS ibid. 27)