Arisian: your ECID is easy to find. It does not change with the OS version, it's hard-encoded into your chip. The easiest way to find it is probably just to plug your phone in and run TinyUmbrella, which will tell you your ECID. You can also put your phone in DFU and check it out in a device profiler.
But finding your ECID will not help you. It is not possible to generate your own SHSH just by knowing the ECID. SHSHs can only be obtained from Apple's server, because they have to be signed using Apple's
private key. This is why your SHSH for a firmware version can only be obtained while Apple is still signing that version. SHSH stands for
signature
ha
sh, and is just a technical term for an encrypted signature attached to a message (in this case, the message authorizing installation of a version of the iPhone firmware).
The SHSH is not saved anywhere on your device or in a backup. It is used only briefly to authorize an installation, and is requested anew for each installation. It is different for each version of the firmware. TinyUmbrella can save your SHSH as it is returned by Apple, but only if you request it while Apple is still signing. Same for Cydia. They take advantage of the fact that Apple failed to include a time check in their authorization scheme, so the same SHSH is returned each time you request the same version. This was really poor security design on Apple's part, since it make it possible to spoof Apple's server as long as you cache your SHSH for each version while Apple is still signing.