Content-wise I didn't really add any music, except for some orchestral sound effects (cymbal rolls, string slaps) here and there. "Remastering" is a very broad term, so here's what I did:
Maybe you guys know the concept of a wavetable or a soundfont, wheras the notes a MIDI track contains are played back using samples of pre-recorded instrument sounds. The sample libraries I used (EWQLSO and GPO4) are a bit more sophisticated than what soundfonts are capable of, adding many more functions like different playing styles (legato, staccato, etc.), different instrument sounds depending on playing volume and many controls to shape the sound of a note while it's played.
Carefully assigning the right instrument and playing style to every line of notes in the Tie Fighter MIDIs took the longest time with this, so I hope it sounds as orchestral and "un-synthy" as possible. Of course, there are bigger, better and more expensive sample libraries (not to mention better musicians than me), but I'm quite happy with how they sound now.