Although they are legendary Pokémon, there are 5 Pokémon in Pokémon Platinum that will roam the land of Sinnoh once their event has been activated. The best way to track them down is to go between two routes quickly until they are in the same one as you. Three of them originally are not native to Sinnoh

Unlike the 2nd and 3rd generation games, the running Pokémon in Platinum are detectable using the Marking Map Application on the Pokétch. With this, you can easily pin down the Pokémon you want and just wait until its in the route you want it to be. Then you can pounce and try your luck at capture
The three Legendary birds; Articuno, Moltres & Zapdos are all obtainable within the same game of Pokémon Platinum. Once you have the National Dex and have been to Pal Park to see Professor Oak, go to his house in Eterna City. When there, he will tell you about the birds and how they've been spotted in Sinnoh. After that, if you check your marking map, all three are in Sinnoh. Their stats are as follows;

Lv. 60 Lv. 60 Lv. 60

Mesprit

After battling and qwelling Giratina, the three legendary Pokémon will be scattered around Sinnoh. Positioned in Lake Verity is the Pink Pokémon in the trio, Mesprit. Once you go to battle him, he runs off. This time his location is not registered in your Pokédex but rather in the Map in your Pokétch. He will appear randomly in the grass. It is at Lv. 50

Lv. 50

Cresselia

After getting the National Pokédex, if you go to the ship in Canalave City, you will have the ability to go to Full Moon Island in order to help heal the Sailor's child. On this island, you will find Cresselia. Once you talk to it, it will run and roam the grasses of Sinnoh. It is at Level 50

Lv. 50