It is Tom that I met yesterday.

[tzfujimino]

I met Tom yesterday.
1. It is/It's Tom that I met yesterday.
2. It was Tom that I met yesterday.

Is #1 unnatural/ungrammatical?
(I'm not really sure which tense I should use in this construction.)

 

[Rover_KE]

I'd only use #2.

 

[slevlife]

Both sentences are grammatical (although you should use “who” instead of “that”), and both are unnatural.

Natural: “I met Tom yesterday.”

In response to a question:
A: Who did you meet yesterday?
B: (I met) Tom.

What is the context in which you wish to say this?

 

[tzfujimino]

Both sentences are grammatical (although you should use “who” instead of “that”), and both are unnatural.

Natural: “I met Tom yesterday.”

In response to a question:
A: Who did you meet yesterday?
B: Tom.

What is the context in which you wish to say this?

Thank you, slevlife.
I was merely trying to express the original sentence by using the "It is ... that ..." construction.
The context would be something like this:

A: Did you meet Ken yesterday?
B1: No. It's(?)/It was Tom that I met yesterday.
B2: No. Tom is(?)/was the one (that/who) I met yesterday.
B3: No. Tom.

B3 is the most natural, I suppose.
Should I use "was" in B1 and B2?

 

[jutfrank]

It's most likely that a speaker would be thinking about the past (the utterance would be accompanied by a memory of the event), in which case he'd use was.

 

[5jj]

I have no strong objection to 'that'.

 

[Tdol]

(although you should use “who” instead of “that”)

That is fine in BrE.