The best way to deal with the dust problem obviously is to keep the dust from getting to the model in the first place. If you’re proud of a model and want it to last, you need to put it in a case.
If the model isn’t very big, quite a few reasonably-priced, ready-made cases are on the market. Trumpeter and various other companies offer them through hobby websites. Such cases are made of injection-molded clear plastic, with black plastic bases.
The big problem with these things is that the plastic has to enter the mold somewhere. Every one of the cheaper ones I’ve seen has, in the center of its top, either a conspicuous blob of plastic or, in the Trumpeter ones I’ve seen, a conspicuous rectangle where the blob was sheered off. Such cases are fine for simply protecting the model, but not so good for display in a living room.
The best little cases I’ve found are made by a company whose name my senile brain can’t remember (I’ll check when I get home this evening) [see later post, below] and are sold by the A.C. Moore Arts and Crafts chain. I’ve bought a couple of them. Each has four circular ejection pin marks, about 1/8" in diameter, in the corners of the top. I might not have noticed them if I hadn’t been looking for them. It might well be possible to get rid of them with rubbing compound; I haven’t tried it. They come in a wide variety of sizes. Some are intended to hold 1/18 or 1/18 diecast car models; the smallest one is designed to hold a baseball, and the largest a football. Some of the bases are plastic; others are black-laquered particle board. The prices are a little higher than the competitors’; the biggest, if I remember right, costs about $40.00. If you have an A.C. Moore’s within driving distance (I couldn’t find the cases on the company website), and your model will fit, these things are worth checking out.
For a good-sized sailing ship there are three obvious options. One is to buy a curio cabinet at a furniture store. My wife and I found a nice one (about five feet high, with three glass shelves) for about $150.00. It holds about a dozen of my finished (not very big) models.
Option 2 is to buy a kit to build a case. Model Expo and Bluejacket both sell such kits; I imagine there are other sources too. Bluejacket offers custom kits, made to the customer’s required dimensions. They aren’t cheap; a case for a 1/96 Constitution would cost between $300 and $400 (not including the glass or plexiglas, which you’ll have to buy locally). But if you think carefully about it you’ll probably conclude that your model is worth it (if your Significant Other will go along with the concept).
The third option is to build a case yourself. That isn’t exactly cheap - but a lot cheaper than the big kits. You need to start with a good design, which you can work up yourself if you enjoy such things. (I’ve encountered several case designs in books, but I can’t say I’ve found one I like.) The most important tool in making a case is a table saw. You also need some means of cutting tight miters (though I strongly recommend keeping them to a minimum - on grounds of strength). To make a really nice-looking case, a router is highly desirable. I bought a little Ryobi “trim router” at Home Depot for about $100; it meets all the needs I have in model building. Lee Valley sells a series of beautiful little miniature molding bits that are just the ticket.
I strongly recommend putting any model on which you’ve invested considerable time and effort in a case. The initial cost may be off-putting, but think how many hours you’ve invested in the model. Dust will wreck it eventually. A cat or a two-year-old can destroy it in a few seconds.