Having just done this, I thought I'd write it up because it worked well but I hit a lot of dead ends and almost payed a hell of a lot more for a worse service. I didn't ship any furniture, TVs or big items, so this method is for a small or medium sized move.
What I did was ship 9 boxes of various sizes for a total of 225KG from Dublin to Narita airport as unaccompanied baggage. This cost me just over 700EUR with K International Freight, including 40EUR to come pick it up from Crumlin. I dealt with Kevin who was helpful, prompt to give a quote and answer questions. They also reinforced some of my less well done packaging, without which I suspect some of my stuff would still be littering the floor of a warehouse in Dubai. The boxes were shipped with Cathay Pacific and took about 3 days of flying via Manchester, Amsterdam, Dubai and Hong Kong. They were trackable all the way. We rented a van in Tokyo, got various bits of paper stamped by customs and loaded the boxes up. The airport part of it took about 1 hour in total, I would not like to have done it without a Japanese speaker.
Less than a week after I arrived, we had all the stuff. We could have had it sooner but I only finished packing at 4am - 5 hours before I got on the plane! Also I was happy to be a bit rested and settled in before organising the pickup and wanted to avoid any complications where my flight was delayed and the boxes arrive before me and need to be stored. I never figured out how long they would hold it for free or how much storage might cost but the Cargo Terminal in Narita is a busy place, so my guess is "not long" and "lots". I also never figured out what would happen if it arrived on the weekend. The Cathay Pacific website says customs "office ours" are Mon-Fri.
I hadn't heard of unaccompanied baggage until I was on the plane to Narita and filling out the customs form. It had a space for how many pieces of unaccompanied baggage I had, so I filled that in and confirmed with the customs guy in Tokyo that it was appropriate. I needed to fill in 2 copies of the form, one he kept and the other he stamped and I presented that when picking it up. I contacted Kevin and asked him to mark the boxes as unaccompanied baggage, which he did. I assume other countries have the same concept, but I've never seen that on a customs form before.
As for other solutions, I looked at lots of moving companies and got a range of quotes, up to many thousands of EUR. Some of the companies offered a full service, they would come and pack your whole house up and deliver it door to door. This was not what I wanted, others ranged in between. Some companies had to be harassed to actually quote me. Others wanted a list of all items in order to quote me! All were far more expensive than K International. There were even some who would put my stuff on a boat for 8 weeks and charge me a small fortune for it.
The 2nd most reasonable option was An Post who cost 145EUR for 20KG but have some tricky size restrictions on the parcels and I also don't trust them too much - according to their website, a parcel that was delivered 4 weeks ago, still hasn't arrived!
Another pretty reasonable option is Vigin's extra baggage service which charges about 100EUR for each extra bag up to 23KG (1st extra bad is only 40EUR). Since my flight started in Dublin with Aer Lingus, I could not use that. It took a bit of work to get a straight answer on that but eventually I got confirmed that I would have to pay Aer Lingus 9EUR per KG for the Dublin to London leg. Given the chance, I would have shipped it this way and avoided 2 trips to the airport but it was not to be. Fuck you Aer Lingus, if you're going to do connecting flights (unlike Ryanair) you cannot avoid checked in baggage, so by charging penal rates you're just doing yourselves out of business.
I suspect other freight forwarders would have similar prices but they do not seem to be common knowledge or targetting the "moving your house" market. I only found K International because I phoned Virgin Cargo (to see if I could bypass Aer Lingus) and they told me they don't deal directly with the public and pointed me at K International.
The only thing I regret was that I tried to pack things into the smallest number of boxes possible. This made it somewhat cheaper but really wasn't worth it. Most of my boxes were 50cm cubed (from Elephant Storage). Freight is charged by weight or if the density isn't high enough, it's charged by volume. Take the volume in cubic cm and divide by 6000 to get the "volumetric weight", you are charged for whichever weight is higher. So I just needed to make each of these boxes at least 21KG to avoid paying by volume. I did better than that but I spent a lot of time dicking around and moving stuff. I also made too many trips to the box shop. I was always sure I needed just 1 more box, I should have just bought lots and returned the ones I didn't use. I optimised for money but at huge expense of time. Lesson learned the hard way (45 min sleep before leaving for the airport and a mess in the house that my family very kindly took care of).
Also, shipping by sea tends to be no cheaper than air. I imagine if you get a container and fill it with your house and car it probably works out better but for a small move, air freight seems to be much cheaper.