I'm still learning about composing and orchestrating Neo-Classical Music (think a sound track for a Netflix documentary), but along the way I've learned some really useful tips. When it comes to composing neo-classical music, the chord structures and melodies really aren't that different than in the pop/rock context. However, the sounds palate you're using, and the rhythmic differences lend it a much more grand and graceful air.
Because there are no drums when you compose and orchestrate neo-classical (generally), you need to put more emphasis on how your chords flow and change into each other. In these videos, I'm using Spitfire Audio's solo strings. They're expensive but they sound amazing.
Tip: using a piano can really help add a bit of extra rhythm and swing.
Composing and Orchestrating Bass and Cello for Neo-Classical Music
This video shows me orchestrating bass for the piano part, if you watch, you'll see how I apply many techniques of a rock n' roll bass, but in a new context.
The other thing you'll notice is that, when orchestrating for neo-classical music, each instrument usual takes a single note from a piano chord and plays it.
For example, if you're playing a C major on a piano (C-E-G), then you might arrange your strings like this: Bass (C), Cello (E), Viola (G). It's also okay to have each of those instruments playing octaves or fifths - i.e. bass playing two Cs or C and G.
Composing and Arranging Viola and Cello for Neo-Classical Music
The fun comes in as you add different rhythms to each of these instruments, and perhaps start to add the occasional passing tone. In this video you'll see how even though the chords are fairly well set, experimenting with leading tones and applying just a little bit of chord theory allows me to fill out the viola and cello parts and bring them to life.
The viola and cello add a lot of the harmonic complexity to neo-classical music, but they also help carry the rhythm as I show in the video.
Neo-Classical Arrangement tip: Don't be afraid of switching which instrument plays the third or the fifth (or the octave, either)
Composing a Neo-Classical Melody
Composing a melody for neo-classical music isn't too different from any other genre. Typically you'll use a violin or viola to play the lead portion.
The easiest way to create a melody is to look at your chords. Then try to arrange notes on a violin that connect the chords in a conversation. You can also considering adding a counterpoint to the pre-existing melodies and phrases that have emerged earlier in the arranging process.
And of course, you'll want to clean up the midi notes after you've played everything live to give it a more accurate sound.