In Emerald, the PokéNav has been upgraded. The Trainer Eye has been replaced by something called an Entry Call. This still has the functions of the Trainer Eyes in them, but they also have another function
You can use it as a phone, you can call up whoever you need and get information from them. Sometimes they will call you up and you will get items or they will say they want to battle you

Click Below to view the rebattle sets of the people in the Entry Call. After the 1st Battle, the Gym Leaders Battle you in Double Battles:

May May May Brendan Brendan Brendan
Roxanne Brawly Wattson Flannery Norman Winona
Liza & Tate Juan Sidney Pheobe Glacia Drake
Wallace Wally Steven Prof. Birch