swear by

He swore by all the gods

He swore by his mother's memory

He swore by a breakfast of prunes and lemon juice.

I found the following meanings from the dictionary.com :

swear by,
a.to name (a sacred being or thing) as one's witness or guarantee in swearing.
b.Informal. to have great confidence in; rely on: He swears by his dentist.
c.to have certain knowledge of: I thought I saw him leaving, but I couldn't swear by it.

I don't think any of the above meanings appropriate in my three sentences. I may be wrong.
Please help me.

the last one is funny!:-D

the meaning of 'swear by' in your sentences is about being very sure, confident about smth

I would say your first two sentences are meaning "a," and the last is meaning "b." Or the last could be meaning "c"---clearly, this person has great confidence in the, er, invigorating power of his usual breakfast, and he must have certain knowledge that it works, day after day. :)