Verb after preposition

Is it correct to write this: "... rely on emulating techniques"? I must write the emulate verb in gerund because it is preceded by an preposition, right?

The whole sentence is:

These systems usually rely on emulation techniques, such as interpretation and dynamic binary translation, to execute guest application code.

Isn't it true that always that a verb appear after a preposition the verb must change to gerund form?

There are quite a lot of verb + preposition combinations able to take an -ing form, and rely on is certainly a commonly used example. Though it might be argued that the actual -ing form used should be called a gerund, it would be less contentious to simply call it an -ing form (somewhere along the verb - noun cline). Thus We can rely on him going / We can rely on his going are both acceptable, as are we must gamble on their finishing the bridge / we must gamble on rapidly finishing the bridge.

However, now you've told us you've replaced the original word 'emulation', it becomes clear that this (verb + preposition + -ing form) isn't the construction involved. The original 'emulation' was correct - it's being used as a noun-modifier (ie adjectivally) here.

You need the whole sentence. As it stands, emulating could be correct, or it might need to be emulation.

"The success of the simulation tends to rely on emulation techniques rather than direct access."

"The ability of the flute player can be affected by their ability to rely on emulating techniques heard previously."

I must write the emulate verb in gerund because it is preceded by an preposition, right?

Strictly, your use of emulating is as a present participle. The difference is minor in English, since the gerund and present participle form are the same word: the -ing form.

The gerund lets a verb phrase act as a noun phrase ("I like emulating" would use it as a gerund, because the X in "I like X" would normally be a noun phrase).

The present participle has a few different uses, and the one here is to use it to modify a noun, much as an adjective would. Here you modified the noun techniques to form "emulating techniques".

Again though it doesn't matter to the clause, because they're both the -ing form. (The verbal noun is different again, and is also the -ing form).

And your clause is indeed valid: We can break "These systems usually rely on emulation techniques" into these parts:

[These systems] [usually rely] [on] [emulation techniques]

These is a determiner in this use, and systems a noun. Together "These systems" is a noun phrase.

Usually is an adverb, and rely a verb, with "usually rely" being a verb phrase.

On is a preposition.

Emulation as described above is a present participle - in its adjectival use - and techniques is a noun. Together they are a noun phrase.

So the grammatical structure is of "[noun phrase] [verb phrase] [preposition] [noun phrase]", the same as the simpler "Systems rely on techniques". By seeing that that simpler form of the same structure is valid, we can see that your clause is valid.

Isn't it true that always that a verb appear after a preposition the verb must change to gerund form?

Well, you can have the gerund or the present participle in that position, but again they will be the same word in English.

I can't think of any exceptions (except arguably the to in "I am going to see", but in this use to is a particle, not a preposition).