The explanation is that Chazal (Bava Kama 92a) say, "Whoever davens for his friend, and he needs that matter, he is answered first." This isn't only in regards to tefillah. Also, whoever does a favor to his fellow man, and he needs that matter, he will be answered first. So, helping someone find a good shidduch is a segulah that you will find good shidduchim for your children.
7. Reb Shlomo Zalman Aurbach zt'l would tell shadchanim that they are occupied with the greatest chesed one can do. Reb Shlomo Zalman, himself, spent many hours making and finalizing shidduchim because of the greatness of this deed. (Shalmei Simcha p.4).
Many people shrug off this responsibility by saying that they aren't shadchanim, and they don't know what a shidduch idea is worth suggesting. Furthermore, even if they do come up with a good idea, they don't know how to iron out the issues that will inevitably come up. They are also afraid of insulting people by suggesting an unsuitable shidduch. So, they stay away from the entire matter and leave the world of shidduchim for the shadchanim. But the truth is, there are ways to overcome these obstacles. When they have an idea, they can share it with an experienced shadchan. If the shadchan thinks it might work, he can suggest it.
Furthermore, the claim that making shidduchim is solely for "professionals" isn't valid. Many shidduchim were suggested and carried through by amateurs, such as friends, family, or neighbors, who came up with an idea. Especially if it is for an older single, or for a family that has a line-up of older children waiting for their suitable shidduchim, one should think about their tzaar and do everything to try to help them. On the other hand, they shouldn't offer any idea that comes to their mind, because if it isn't suitable, it might cause tzar. Whenever in doubt, one can go to someone with experience in the field of shidduchim for advice, or to have them take the shidduch off your hands and take care of it themselves.
8. The Gemara (Moed Kattan 18:) proves "from Torah, Nevi'im, and Kesuvim" that shidduchim are destined from heaven. From the Torah, טוב או רע אליך דבר נוכל לא הדבר יצא 'מה ויאמרו ובתואל לבן ויען, "Lavan and Besual said, 'The matter has emanated from Hashem. We cannot speak to you either bad or good.'"
In Navi it states (Shoftim 14:4) regarding Shimshon, היא 'מה כי ידעו לא ואמו ואביו, "His father and mother didn’t know that it was from Hashem."
Also, in Kesuvim it states (Mishlei 19:14), משכלת אשה 'ומה אבות נחלת והון בית, "A house and wealth are bequeathed by fathers, but an Intelligent woman comes from Hashem.'"
Other Mitzvos Related to Shidduchim
2) It states (Yeshayah 45:18) ֶׁבֶתלָש ּבְרָאָה תֹהוּ לֹאּיְצָרָה, "He did not create [the world] for emptiness. He created it to be inhabited." This mitzvah is for one to attempt that there should be a lot of people in the world. Working towards making shidduchim is therefore a fulfilment of this mitzvah, as well (see .מא לגיטין אלישב ש"מהגרי הערות).
3) Helping someone find his shidduch can also be included in the mitzvah of tzedakah. It states (Devarim 15:8) אֶת תִּפְת ַּח ַפ ָתֹח כִּי לוֹ יֶחְסַר ֶׁראֲש מַח ְסֹרוֹ דֵּי ... לוֹ ָיָדְך, "You shall open your hand to him... whatever he is lacking..." Rashi says that this refers to a wife, to help him get married, which is included in the mitzvah of tzedakah.
4. Above all, he is performing the mitzvah of חסדים גמילות, to do deeds of loving-kindness. Helping someone get married is the greatest kindness one can do for another.
