There is a standard way of performing wired screen mirroring, from the USB port of an Android phone/tablet to a HDMI-input screen (e.g. TV or a portable screen), and that is through an MHL cable, provided the phone supports it. Most of the premium phones do support MHL. An iOS device would require a proprietory Lightning to HDMI Adapter.
One major problem with MHL is, it does not support screen rotation, i.e. screen mirroring in portrait mode. Understandably so, because there’s no way for MHL to predict whether your mirrored display is positioned in landscape or portrait mode, so it assumes landscape always, which is the norm.
The way around this is.. to not use MHL altogether. While searching for a solution on Taobao, I found the GoBiggeR dongle. It runs an App to perform the screen mirroring. Interestingly, the GoBiggeR dongle also has plug-and-play support for iOS devices whereby you don’t need to install any additional software to perform the screen mirroring.
There are wireless solutions that also support Portrait mode mirroring, and they are cheaper and probably work well too, but those can never compete with a wired solution for guaranteed signal stability. The GoBiggeR dongle, at 158 Yuan (S$32.70) is relatively expensive in comparison to a wireless dongle (like this one which is 98 Yuan or S$20.30), and much more expensive than an MHL dongle (such as this one which is only 45 Yuan or S$9.3).
In any case, the GoBiggeR dongle is still reasonably priced, and serves the purpose well where you need portrait mode mirroring or where your phone does not support MHL. The only caveat for it to work is having USB 3, which is usually the case for phones using Type-C USB jack anyway.
Update: If you just want to mirror your Android device to your PC/Laptop, there is a free solution in the form of scrcpy, which supports viewing in either portrait/landscape orientation. It even relays mouse clicks to the actual Android device. There are many tutorials out there on how to set it up and it’s easy (tip: you might need to set the display resolution with the -m command switch).