It's a bit of a crap shoot, but I've booked dozens of international frequent flyer flights over the past 10 years and most for relatively low mileage.
That isn't always possible....over the XMAS holidays this year I flew my son out from DC to Manila (where my DW & I currently live) and had to use 120k miles on Delta (rather than the 60k minimum). But that WAS the holidays.
Generally, I've found Delta the hardest to use mileage to get good deals on tickets, but they tend to be quite good for upgrades....For 50k miles, for example, you can get a round trip upgrade from coach to business from Manila to DC on Delta's newly upgraded (and very plush) business/first flatbed service (you also have to pay about a $500 premium on the cheapest ($1500) coach ticket.
United has been very good for cheap mileage flights within Asia and it also has a very easy to use website. You'll see tons of flights from Bangkok to Manila to Singapore to Tokyo, etc.; on Singapore Air, Thai Air, Asiana, etc.; typically for 12,500 miles each way in coach and 17,500 in business...and stops are included! My wife and I are flying roundtrip from Manila to Denpasar (Bali) next month on Singapore Air with a stop in Singapore for 35,000 miles roundtrip (each) way in business! (And Singapore's international business class is amazingly good!)
From the U.S. I've also had good luck on flights across the Atlantic to Europe, in both business and coach. I even lucked out once to score roundtrip First Class tickets on Lufthansa to Toulouse and Barcelona for my honeymoon for 100k, but that took some finagling to transfer miles to AirCanada, which had some kind of a special deal. I must say, it was a gas though getting picked up on the tarmac in a limo in Munich to transfer to and from the first class lounge!
But typically, good deals to Europe are ONLY available in the off-season and you have to have some flexibility on dates and destinations. In recent years I've had better luck (even during the high season) using mileage to upgrade coach tickets to business (for anywhere from 10k to 20k miles each way, and once with a $400 rd trip supplement to get in the right fare category).
It does take some perseverance....and it helps if you're a premium member and can use their book desk....the web sites can be somewhat opaque, particularly for partner airlines.
But even when you get frustrated, you can sometimes get cheap paid seats on many of the new budget carriers (particularly in Asia and Europe) and sometimes on the traditional careers trying to compete... My wife and I were able to get $200 round trip tickets to Siem Reap (Ankor Wat), Cambodia and Hong Kong from Manila on Cebu Pacific (and they're sometimes half that) and I lucked out another time and got $355 round trip business class tickets on Cathay Pacific from Manila to Beijing (I almost purchased what I thought were well priced coach tickets for $350, but luckily decided to check business before clicking the mouse!).
So, keep trying! And good Luck!