OK, thanks to @David Weldon, I can provide a fairly complete answer to this issue:
Backing up and restoring your local MongoDB for Meteor users (OSX)
Backup:
1) Your app must be running, so start up your Meteor server.
2) In a terminal window (NOT in the meteor mongo shell), enter: mongodump -h 127.0.0.1 --port 3001 -d meteor
This will create a 'dump' directory inside your home folder (your name under Users).
3) If you get a 'command not found' message, you probably just installed Mongo as a part of Meteor, meaning you don't have the mongo command line tools. Use a package like Homebrew to reinstall Mongo and you will have the command line tools. This will also add the correct PATH information to your system, so that it can find the tools.
Restoring:
1) From MiniMongo shell (run ‘meteor mongo’ inside your Meteor project dir), enter:
db.[collectionName].drop(); //repeat for all collections you wish to restore
2) Then, from a terminal window, enter:
mongorestore -h 127.0.0.1 --port 3001 -d meteor dump/meteor
Caveats:
The individual documents will not necessarily be in the same order after they are restored. So you need some way to sort documents that need to be presented in a certain order.