What are some options for finding my lost companion Veronica, besides a manual search?

Fallout Wikia has some tips on recovering lost companions who do not appear in either their original location or the Lucky 38. I have not had this problem myself so cannot test.
Update: I can confirm the Vault 22 method worked for me; successfully recovered Rex (on PC).

For Consoles and PC

Here the given trick is to go to Vault 22 and use the central elevator (requires repair skill level 50).
Choose to go to Level 5 - Pest Control.
The missing Companion(s) may be waiting there at the exit of the elevator, you may need to talk to them and ask them to follow you (ie, they may be stuck in wait mode).

For PC

This involves using the console commands, I highly recommend saving before messing with the console, and as per Xantec's comment you should be aware this will disable Steam achievements for that play session (ie, you need to fix the game then save and restart).

Here <red_id> is an internal number for the companion - for Veronica this seems to be 000e32a9 - you can get the ID's of others from the Wikia site as well.

This will move the companion to your location:

prid <ref_id> 
moveto player 

This will move you to the companions current location:

player.moveto <ref_id> 

If these don't work the recommendation is to kill and resurrent the companion. First use these two:

prid <ref_id> 
OpenTeammateContainer 1 

This should give you their inventory windows - empty it into your own.
Then do the following, and hopefully the companion should be back:

moveto player 
resurrect 1 
disable 
enable

I wanted to post a comment, but I'm not able to yet. I hope someone will find this post helpful. I would like to add that, as far as finding lost companions in Vault 22 is concerned, going there is not a solution in every situation. I lost Veronica while diving in Lake Mead - I managed to get ashore and teleported to another location, and she stayed in the water. I thought she would appear in the new location, but she didn't. Going to Vault 22 didn't help - she appeared by the elevator, but she would not follow me outside, and while talking to her there, she would move her hands as though swimming. I had to get back and try to find her, but it was a futile attempt, as I couldn't find her anywhere. I guess loading a previous savegame is the only solution for those who lost their companions under water.

Another Option could be to look for an secure Place (e.g. Lucky 38) and rest there for several hours.

In most cases the Companion returns to you after 48 hours of rest.