In previous games, to get rematches with trainers, you used the VS Seeker to see if the trainers were willing to battle. In HeartGold & SoulSilver however, the rematches are done a different way. Firstly, only a few dozen trainers in Kanto & Johto are capable of being battled again.

In order to get the rematch, you have to receive the PokéGear number from the trainer in question. Then, on a certain day, you will need to ring the trainer in question to organise a rematch. It is not guaranteed that a rematch will be discussed when you call but keep trying and you should get it. Below is a list of all the trainers, battleable on Saturday, and their teams including their first team and each team's increase in level. Click the other days to go to their page

Monday | Tuesday | Wednesday | Thursday | Friday | Saturday | Sunday

Saturday

Time	Location	Trainer
Morning 4am-10am	Johto - Route 34	Camper Todd
Teams First Battle Camper Todd Psyduck Level 14 Second Battle Camper Todd Geodude Geodude Psyduck Level 17 Level 17 Level 31 Third Battle Camper Todd Geodude Graveler Golduck Slugma Level 23 Level 33 Level 36 Level 32 Fourth Battle Camper Todd Graveler Graveler Magcargo Golduck Level 36 Level 44 Level 54 Level 56
Morning 4am-10am	Johto - Route 34	Youngster Ian
Teams First Battle Youngster Ian Mankey Diglett Level 10 Level 12 Second Battle Youngster Ian Mankey Dugtrio Level 27 Level 33 Third Battle Youngster Ian Primeape Dugtrio Level 38 Level 40 Fourth Battle Youngster Ian Primeape Dugtrio Level 47 Level 56
Day 10am-8pm	Kanto - Route 13	Hiker Kenny
Teams First Battle Hiker Kenny Sandslash Graveler Golem Level 27 Level 29 Level 33 Second Battle Hiker Kenny Onix Graveler Golem Sandslash Level 16 Level 33 Level 37 Level 32 Third Battle Hiker Kenny Sandslash Graveler Golem Onix Level 42 Level 37 Level 44 Level 46 Fourth Battle Hiker Kenny Sandslash Graveler Golem Steelix Level 46 Level 44 Level 49 Level 54
Night 8pm-5am	Johto - Route 46	Picnicker Erin
Teams First Battle Picnicker Erin Ponyta Oddish Level 17 Level 14 Second Battle Picnicker Erin Gloom Rapidash Level 32 Level 41 Third Battle Picnicker Erin Bellossom Sunflora Rapidash Level 46 Level 39 Level 48 Fourth Battle Picnicker Erin Cherrim Sunflora Bellossom Rapidash Level 42 Level 46 Level 49 Level 53
Night 8pm-5am	Kanto - Route 15	Twins Kay & Tia
Teams First Battle Twins Kay & Tia Quagsire Quagsire Level 41 Level 41 Second Battle Twins Kay & Tia Quagsire Quagsire Level 48 Level 48 Third Battle Twins Kay & Tia Quagsire Quagsire Level 53 Level 53 Fourth Battle Twins Kay & Tia Quagsire Quagsire Level 55 Level 55
Night 8pm-5am	Kanto - Route 27	Bird Keeper Jose
Teams First Battle Bird Keeper Jose Farfetch'd Level 40 Second Battle Bird Keeper Jose Farfetch'd Level 44 Third Battle Bird Keeper Jose Farfetch'd Farfetch'd Level 38 Level 40 Fourth Battle Bird Keeper Jose Farfetch'd Farfetch'd Farfetch'd Level 50 Level 52 Level 53