By definition of the audio range for humans, beyond 20kHz is beyond audio. There are audio equipment designers such as Rupert Neve who believe the range could be wider, but this is not necessarily based on strong evidence. The vast majority of audio equipment therefore is limited to this maximum frequency, and you will never be able to do it. Some professional-grade audio equipment may allow you to get past this, although you might need to do some mods. That's the TLDR - full explanation to come.
According to the Nyquist-Shannon Theorem, sampling at any frequency higher than double the maximum signal frequency will give you the exact signal out. For various reasons, CDs standardised on 44.1khz sampling, which of course is more than twice the maximum audio frequency, and the majority of consumer electronics also uses this sampling frequency. From Nyquist-Shannon, it is mathematically impossible to measure signal frequencies above 22.05kHz with equipment sampling at 44.1kHz.
This isn't the end of the story though, because sampling is only half the battle. If you do put in frequencies higher than the Nyquist limit, it turns out that you get a "reflected" frequency coming back - so if you put a 27kHz signal into audio equipment sampling at 44kHz (Nyquist limit of 22kHz), you'll actually measure a signal at 17kHz, with the frequency "reflecting" back from the Nyquist limit. This is called "aliasing" and it plays merry hell with your signals, of course, so the other half of sampling is to have a strong enough filter on the way in that you kill off those frequencies. We call this an "anti-aliasing filter". (You may have seen "anti-aliasing" as an option on your graphics settings in games. This is what it's doing.)
This is why early CD recording didn't sound as good as vinyl, a myth which still persists today. The problem wasn't anything to do with the CD format, it was entirely to do with how they sampled their signals. With only 2kHz of "spare" frequency between the top of the audio range and the Nyquist limit, it's very hard to get a strong enough filter to kill off those higher frequencies without affecting the top end of the audio range. Designers have had this nailed for some time, but there's always some trade-off with what it does to the top end of the audio. Mostly it's not anything to worry about though.
In the quest for the best sampled signal though, and with more space to store larger files, many designers of pro audio equipment have extended the sampling frequency to 96kHz (or sometimes 88.2kHz, which is convenient for downsampling to the CD sample rate). This gives you a Nyquist frequency of 48kHz (or 44.1kHz). With 24kHz/28kHz of "spare" frequency to play with, the anti-aliasing filter doesn't have to be as strong and it won't trample on the higher audio frequencies. You won't find this in consumer-grade electronics like phones, but you'll find it in studio equipment from people like Mackie and Focusrite (or even Behringer) at the affordable end of things.
So if you need to sample at these higher frequencies, you absolutely can buy something with 96kHz sample rate and expect to get a sampled signal containing your frequencies of interest. The downside of course is that you're running in the range where your signal is being filtered. For the filtering done in hardware (individual resistors and capacitors on the board), you may be able to do hardware mods to change the filter cutoff. If you talk nicely to the company, they may even point you in the right direction.
The more practical alternative though is to work out the filter roll-off characteristics and try to compensate for it. Using some sort of audio software (e.g. Audacity) you can apply a suitable high-frequency boost filter, and hopefully you'll get those frequencies back. This won't be very accurate with 16-bit sampling (like a CD), but most equipment at this kind of level uses 24-bit sampling (which has been best practise in studios for at least 20 years) so you should still have enough signal to work with. This might sound a bit of a kludge, but it's exactly what record decks have done since forever (using an RIAA filter) to deal with the inherent crapness of vinyl as a playback medium, so you're in good company. Of course boosting those frequencies will boost noise at those frequencies too, so the higher you go, the more your signal will start to get drowned in noise. You should be OK in the low-mid 20s, but I'd expect you to start losing your signal beyond 30kHz.
There are other alternatives, of course. You could abandon audio equipment entirely, and manufacturers such as National Instruments produce a range of industrial measurement equipment which will sample whatever you want. At this point though you really do start to pay for the fact that you're trying to do something which is non-standard.
As Juan noted too, you do also need something which will pick up this frequency in the first place without distorting the signal and keeping a pretty flat frequency response. Again, your regular microphone won't do that. Phones and the like are tailored for reproducing voices, and as a soundman I can tell you that what makes a voice sound clear is very much not a flat frequency response! Even for mics aimed at picking up instruments, they tend to be tailored for the human audio range. For your application, you definitely need a "measurement mic" instead. The Beyerdynamic MM1 is probably the minimum at the low end, up to rather expensive ones such as the various Earthworks mics at the higher end.
I realise this is a rather long explanation, but hopefully it covers the "why" behind the problems you're likely to run into. Good luck!