Get yourself a meter. Some insurances cover it. I'm told that Medicare covers it (if you have Medicare). Test weekly -- or more often if your diet or activities take any drastic changes.
For myself, I've purchased my own meters, I buy my own supplies, and I manage my own dosing. I track dose, INR, and anything else that may influence my INR using a spreadsheet. My records go back more than four years.
I would NOT be comfortable with going to a lab 'every month or so', whether traveling or staying at home. I know that some labs, and some doctors, are content with testing every month or two, but I don't think this is enough. Even some of the machine manufacturers advise to test weekly.
You may be able to find a doctor or clinic that can manage your dosing for you -- just call in your INR, and they'll get back to you with changes (or not). While traveling, it may make sense to carry a few different dosages of Warfarin, in case your clinic or doctor advises any changes, but you should be careful about drastic changes to dosing. It may help to get a seven day pill container -- that way, you'll know if you have already taken your daily dose.
If I had the type of job where I have to travel, I would bring a meter (or two), a supply of strips, my computer or a book into which I would record dosage and INR (and other items that may seem relevant), and do my traveling. I wouldn't let it hold me down.
If your INR is not stable, you may want to wait until it is -- but with regular testing - possibly even more often than once a week until your INR is stabilized -you should be fine to travel.