By following a few simple suggestions, you will prolong the life and appearance of your mutes and enable them to give you many years of trouble-free service and enjoyment.
Inadequate mute bags have been making mute manufacturers a lot of money for a lot of years. The variety of mute bags most brass players use is endless. I have seen fellow trumpet and trombone players carry their mutes in duffel bags, gym bags, and even paper and plastic shopping bags! These do not offer the proper amount of protection for your mutes and their use often leads to unnecessary damage and early replacement. During the years when most of the pioneering mute manufacturers were still in business, players took the availability of these wonderful mutes for granted. Many brass players did not care for their mutes in the proper manner because these mutes were cheap and readily available. Now many are not. Here are a few recommendations for keeping your mutes in pristine condition.
Currently, I keep my gigging mutes in a generic hard plastic case that I picked up at the Container Store for $15. It's perfect. The case is lined with a thin layer of foam rubber, and it protects my mutes while they're in transit from gig to gig. There are other choices of hard cases available as well. Home-improvement stores carry many types of inexpensive hard plastic toolboxes and cases. Also, camera stores offer a variety of lightweight hard plastic cases that can be used for transporting your mutes. I even have a few trumpet students who have purchased vintage train cases through eBay auctions. (Before air travel was common, long trips were done by ship or rail. A train case was an early carry-on, a small hard-sided suitcase that people would carry onto the train for their toiletries and small valuables.)
Also, it's a good idea to keep your mutes separate by having each in its own individual cloth drawstring bag. The drawstring bags used by the Crown Royal whisky makers for their 750 milliliter and 1 liter bottles are perfect for this purpose. If a brass instrumentalist makes the effort to keep their mutes in a drawstring bag within a hard plastic case, it will decrease the possibility of undue damage.
A wide variety of mute stands are available on the market today. Most mute stands clip onto the music-stand shelf. Other mute stands clip onto the center shaft of the music stand or are free standing. Do some online research to find out which mute stand/holder would best accommodate your personal needs. Without a mute stand, a brass player's only alternative is to set the mutes on the floor. This presents a number of potential hazards. When you or your fellow section mates get up to exit the stage, your mutes can be kicked off a riser or into the saxophone section or even stepped on, which in many cases can cause irreparable damage. In addition, when your mutes are sitting on the floor beneath your instrument, they are subject to getting doused by your water key while you are performing. This can be unsanitary. Also, some stage surfaces are quite rough; your mutes can get scratched. Having a mute stand also allows easier access for quick mute changes. From the audience's standpoint, it doesn't look very professional to bend down (and disappear from their view) in order to pick up your mutes from the floor during a performance.
In most cases, mute corks need to be filed so that the mute fits in your trumpet bell properly. For information on how to file your corks, please see the Corks page of this website.
Keeping your mutes in a cloth drawstring bag within a hard plastic case will help prevent your corks from drying out and becoming brittle. Keeping your corks moist helps to keep them supple. Corks need to have a certain degree of flex in order to accomplish their intended purpose. Try to keep valve oil off of your corks. The petroleum distillates in most valve oils will dry them out. Use caution and care when inserting your mute into the bell of your brass instrument. It's also a good idea to breathe warm air into your bell before inserting your mute. The warm air creates a small amount of condensation, which makes your corks very happy.
Appearance is important. Many people say you can judge a person by their shoes. In many ways, this is true. Similarly, you can tell a lot about fellow brass players by the condition of their mutes and other musical accessories. During my playing career, there have been a couple of instances when I have actually witnessed fellow trumpet players using their cup mute as an ashtray! As it turns out, that wasn't a good use for those mutes.
Also, appearance is obviously an important ingredient when presenting oneself onstage and in public. Every so often, I spray a small amount of Lemon Pledge on a mute, and then use an old washcloth to polish it. The minuscule amount of wax in the Pledge will not affect the sound quality or vibration of your mutes.