I think all levels of defeated warlord can yield a summoning bond.  Since the energy recharges several times a day you can just keep defeating the two highest level warlords that your two guardians can kill in one battle.  You can only win a bond when you defeat a Warlord so dont waste your time/energy doing partial battles.  Kill as many warlords as you can.  Look at the battle results and see if you win extra energy from time to time which is a sign that the battles still give you rewards even if you dont gain Experience points.  Then be patient. A bond will drop about every 20 battles.

Vänrikk1 said:

My situation is this: the new attribute to the game, Guardians. I am in a situation in which I have 9 emeralds. I have 2 guardian at max level each. I am unable to gain any additional emerals due to the max level of my guardians, in any manner that I can think of. When I attack war lords, I get not guardian XP points, due to the maxed out guardians I have. I cannot think of a way to play this aspect of the game. Help please?

Here the some print screens:
https://snag.gy/IFXRKP.jpg
https://snag.gy/JD3tTq.jpg
https://snag.gy/pUmc5Q.jpg
https://snag.gy/2zeiHG.jpg
https://snag.gy/sXeNQ5.jpg
AS you can see my guardian attacks to warlords no longer award me any guardian XP points.

This usually happens to people who do partial battles = 'nibble' higher lvl Warlords with low lvl Guardians. It's a same mistake I did right at the beginning. Mikalosos gave you some good advices.

You have to keep using your lvl 15 guardian to hit lvl 8 warlord. Your lvl 20 guardian use to hit lvl 10 Warlord. And repeat until you'll get summoning bond.

You won't get XP, but you will get a summoning bond eventually and then make sure not to do partial battles.

Hit Warlords like this:

lvl 1 Guardian >> lvl 1 Warlord

lvl 2 Guardian >> lvl 1 Warlord

lvl 3 guardian >> lvl 2 Warlord

lvl 4 Guardian >> lvl 2 Warlord

lvl 5 Guardian >> lvl 3 Warlord

lvl 6 Guardian >> lvl 3 Warlord

lvl 7 Guardian >> lvl 4 Warlord

lvl 8 Guardian >> lvl 4 Warlord

lvl 9 Guardian >> lvl 5 Warlord

lvl 10 Guardian >> lvl 5 Warlord

lvl 11 Guardian >> lvl 6 Warlord

lvl 12 Guardian >> lvl 6 Warlord

and so on and so on...

Do you know at what level of defeated warlord I'll start receiving an occasional summoning bond? 

Even lvl 1 Warlord can give you summoning bond

How do you know I'll receive those without getting any XPs? 

I've been in a same situation first 3 days after Guardians got implemented on plarium.com. I've made mistake of doing partial battles, but I got out of it and now I'm doing pretty good with guardians. Scored 1 mln points in last week Guardian XP tournament.