Whether one calls it "matchmaking" or not — and irrespective of that much-abused term and whatever connotations it may carry, whether serious or silly, stressful or scary — parents ought to be actively involved in all of their children's relationships, and all the more so in preparing their children either for holy marriage or for a sacred vocation of celibacy.
Fathers, in particular, must be pro-active in guiding their sons and daughters in a positive direction in all of their relationships. Fathers should be training their sons, by consistent example and deliberate conversation, to become men who will be faithful husbands and fathers, whether in earthly marriage or within the household and family of God. Fathers should be caring for their daughters, also, not only by exemplifying what a godly husband should be like in his own relationship to their mother, but by serving as their God-given head until he gives them in marriage to the man who will become their husband, whether in holy marriage or unto Christ, the heavenly bridegroom, within the life of His Church.
Such pro-active paternal oversight requires more than acquiesence, a nod of the head, and the formal blessing of a relationship that has already developed and become a fait accompli. It means that a father will be training and helping his son to become the sort of man he ought to be, and helping his daughter to discover the sort of man — and the particular man — who may become her husband; or otherwise helping his sons and daughters to discern the possibility of celibacy as a calling of service to the Church and to their neighbors in the world.
No father should attempt to force his daughter to marry anyone against her will, but neither should any daughter marry against her father's will. These things can work themselves out in a wide variety of ways, from "arranged marriages" to modern "dating," but they will not be worked out rightly apart from parental involvement and paternal authority. If a girl's natural father is negligent, wicked, or missing in action, God will yet provide other "fathers" who will care for her, protect her, guide her and direct her. Not as though a girl is helpless, incompetent or weak; far from it; but as the means by which she lives in faith according to the Word of the Lord. Fatherhood is rightly exercised in love, with both discipline and compassion, and with solicitous concern for the well-being of sons and daughters alike. It is not to be taken lightly, nor abdicated by design or default. Fathers are given, by and with and under the Word of God, to guard and protect their children against the wickedness of this sinful world, against the weakness and perversion of the sinful heart, and against the assaults and accusations of the devil.
God has not given any one-size-fits-all pattern for how children are to grow up and become adults, except the pattern of the Fourth Commandment: "Honor your father and mother." That is my pastoral answer, my personal advice, and my paternal admonishment to parents and children alike. Parents must take this seriously, as having both their authority and responsibility from God, to be exercised in harmony with His Word and according to His good and gracious will. Children, likewise, must take the Fourth Commandment seriously as the primary way in which the Lord their God guides and governs their temporal life on earth, especially unto marriage or an adult vocation of celibacy. Marriage will not be for everyone, but chastity is, whether within or outside of marriage. For those who do not have the gift and vocation of celibacy, marriage is the divine gift and vocation within which they glorify God and serve their neighbors in faith and love.
There is no one right age at which marriage should or must happen, nor any one particular set of circumstances that must obtain before marriage. Determining whom to marry, and when, is governed chiefly by the fourth and sixth commandments. Adultery and fornication are always sinful, at any age, whereas getting married with the guidance, approval and blessing of fathers and mothers is truly meet, right and salutary, irrespective of age (within reason and under the law, of course). Getting married at 18 may be exactly right in some cases, whereas getting married at 24 may be exactly right in others; or at 20, or at 30, or whenever. But it grieves me as a pastor to encounter parents who would much rather tolerate, condone, or even encourage fornication on the part of their children, than approve or support their children getting married "too early." The popular humor that glorifies fornication and denigrates marriage doesn't help, of course, but makes it all the more necessary that fathers and mothers teach their children rightly: that marriage is a good gift of God, and that sexual intimacy outside of marriage is sinful and destructive to both body and soul. To live chastely outside of marriage, in service to the Church and to one's neighbors in the world, is also a godly and God-pleasing vocation; and for this, too, parents are key to determining the path that one should pursue.
All of this is undertaken in the confidence of God's Holy Word, which directs children to honor their parents, and calls the hearts of the children to their fathers, and the hearts of fathers to their children. Even at that, there is the more sure and certain confidence of our dear Father in heaven and the everlasting Bridegroom of the Church, in whom we parents and children alike are forgiven and enlivened by grace, unto the life everlasting.