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