While incentives for appropriate levels of labour (and occasional other things) and recognition for behaviour that is virtuous (particularly levels of virtue that are admired by the general public but are distant from mandatory or strongly pushed) are appropriate in some circumstances, honours and recognition are in the general case dangerous and to be mistrusted. Society should be structured and understood to have a flat level of personal status in the general case, any deviations both requiring good justification and being preferably small.
Liberals should also prefer to ignore honours originating in other systems (to the extent that they come from nonliberal value-conclusions) to whatever extent they can. Foreigners in a liberal society should not expect nor recieve honorifics from the demos (and might not recieve it from the state itself), and liberals travelling into a nonliberal society will, at least by their values, be disinclined to take seriously foreign honours (for their own safety or to whatever extent they may find it useful to blend in or be polite, they may go through the motions but should keep an inner distance).
Systems of nobility are not acceptable to liberalism - even when not hereditary, they undermine virtue and dignity of individuals and lead to uneven enforcement of laws.
Entirely precluded in modern liberal societies is hereditary privilege, respect, or other honours. In a situation where a liberal were in an early society, if achieving appropriate education and character in the demos were not possible during one's lifetime, it may be appropriate to have hereditary rule for an ideally short time while transforming society along those lines - a long-term monarchy would not be acceptable then and it is not acceptable in modern times. To avoid corruption of the values of the demos, liberals prefer not to see politics running too strongly in families and should be more reluctant to elect someone from a famility where someone was recently elected than someone from an unrelated family.
In transitional societies that have not yet been organised around a shared concern for the public welfare, particularly those under which there is sex-disparity in ability to work, the limited privileges permissible may include provisions for the welfare of widows or children until they are able to care for themselves.