The matchmaker comes to your tamagotchi at age five, six or seven. Just be careful not to pause your tamagotchi and make sure your tamagotchi has full happy and hungry levels before it goes to sleep.
It is different for each version. For V4 and V4.5, it is 7. For the others it is either 6 or 5.
The matchmaker also comes at specific times, so here is one: 2:99 PM (Really comes at 3:00 PM) The matchmaker will stop visiting your tamagotchi once it evolves into an oldie, which is USUALLY at the age of 10