Estar seguro (de que)
 

No estoy seguro si podré ir contigo.
No estoy seguro de que si podré ir contigo.

I know the first sentence is correct, and I think the second one is, too, but I’m not completely sure.

Many thanks in advance.

The expression is "no estar seguro de", so you may say:

- No estoy seguro de si podré ir contigo.
- No estoy seguro de que podré ir contigo.

And since it's the same subject speaking, you may also say: "no estoy seguro de poder ir contigo". :)

Thanks so much.

So, without the preposition 'de' (i.e. 'de si') the sentence below is incorrect?

No estoy seguro si podré ir contigo.

It is incorrect, yes. You are always 'sure of (seguro de) something (algo)', or you're not sure of it.

Thanks, Rusty. I thought so, too. I ask because a native Spanish teenager omitted the preposition 'de', and it got me wondering...

That's a common mistake. Some people tend to avoid "de" or "que" to avoid incorrect expressions, but they also omit them from the ones that do need them. ;(

Native speakers from every clime and continent make mistakes when speaking.

I've heard the same omission you have, several times. In fact, you'll find that there are those who write the structure with the preposition in parentheses when teaching the construct to others, online.

Here is what the Diccionario panhispánico de dudas site says on the subject:

estar seguro. ‘No tener duda’. La persona o cosa sobre la que no se tiene duda se expresa mediante un complemento introducido por de: «Estoy segura de que la oirán» (Padilla Jardín [Cuba 1981]). En el habla esmerada, no debe suprimirse la preposición: :bad: Estoy seguro que.