If you beat the Elite Four and Champion and go in the Hall of Fame Start looking for her if you want her.
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You can't get Latios in HeartGold. You can get Latias, to get her, talk to the copycat in Saffron and find her lost doll in Vermillion city at the fan club and Steven will be out there when you come out. He will talk about Latias for a minute and Latias will be in Kanto just walking around like Raikou.
nothing.
after that, someone at the battle frontier will tell you about latias and latios. then, latias will start roaming kanto.
In the pewter city museum. to get his attantion you must bring walking latias ( heartgold) or latios ( soulsilver ) with a soul dew from a mystery gift. then he will take you to saffron city. he will talk to you for a while. then he will go back to pewter then show you latios ( heartgold ) or latias ( soulsilver ) outside of the museum. then after you defeat or catch one of eon Pokemon that's the last of him.
The cool legendaries you can get in Soulsilver/heartgold are the following: Lugia, Ho-oh, Raikou, Entei, Suicune, Articuno, Moltres, Zapdos, Mewtwo, Latias, Latios (Latios in Soulsilver & Latias in Heartgold), Kyogre, Groudon, Rayquaza (Kyogre in Heartgold, Groudon in Soulsilver & Rayquaza if you have both).