One of the greatest challenges the European Union is facing nowadays is the current demographic changes. The issue of ageing population is gaining popularity also in the light of economic research. The aim of this study is to examine the perception of mature consumers (understood, for the purposes of this study, as born before 1967) of the quality of property insurance, with a particular emphasis on the claim settlement aspect. Information on how mature customers perceive the quality of insurance is important both from the perspective of insurance companies and insurance intermediaries. The former are developing and improving a tailored range of products for specific customer groups, as competition on the insurance market is constantly growing. Insurance sales have become computerised. Insurance agents have to constantly adapt the methods of acquiring clients to the changing needs of the latter; the needs and perception of insurance products and services differ across age groups. The study was conducted in the years 2016–2017 by means of the CAWI (Computer Assisted Web Interview) and PAPI (Paper and Pen Personal Interview) techniques. The questionnaire was completed by 388 residents of Lubelskie Voivodship whose selection was based on a quota sampling. The results of the survey were analysed with the application of an ordered logit model, in which quality aspects (such as the access to information, availability of the liquidator, etc.) were used as dependent variables, while socio-economic features (i.e. age, sex, place of residence, income, etc.) as regressors. The study showed that in addition to immanent product features, high compensation is most important to the respondents. Respondents perceiving their financial situation as satisfactory tend to assess the technical aspects of the damage liquidation process as less important than those with lower income, while older surveyees perceive the issue of insurance formalities as much more vital than younger respondents.