I had the same question last year. I’m not sure if it makes a big difference but I think I made my cuts parallel to the ground as you suggested.
Not enough time yet to know the effects…
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@applenut Do you mean one side of the female part should be narrower? (That bottom cut is a messy one. I shouldn’t have posted it!) I don’t think that I get my scion cut made thin enough - or long enough, either. Maybe I should try the ‘cutting board’ method.
It’s hard to see - but the ‘top’ side of the branch is narrower. I try to cut closer to the side - not dead center. Not enough? I think the cambium on this one met on the other side.
I also have a hard time keeping the scion where I want it, while wrapping it. 
Try wrapping with the rubber before you cover it with Parafilm. I try to pull the band to almost breaking.
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The scion (male) should be pie-shaped in cross section, with the outer bark where the pie crust would be. I cut mine with a $1 store plastic utility knife, bracing the scion on top of a fencepost or something. long and tapered is what you’re looking for.
The below photos show an incorrect fit
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applenut,
I think her scion and host may be of the same diameter as one another.
For a cleft graft, even if both are the same diameter, only one side should touch, lest the wood in the middle keeps both sides from making firm contact.
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This is a really neat trick
Thank you so much, Andy:+1: