I have an almost-satiny navy tie (RLPL from many years ago) that seems much less shiny when paired with an actual suit. I wear it with an Oxxford navy blue pinstripe suit and a white shirt, but it can look almost too austere in that context. I also have a navy/royal (mid-range of colors) heavy twill tie - it was called 'Ottoman Twill', I think. It is great, and the fabric creates a lot of surface interest. Finally, I have a solid navy Drake's tie which is fairly matte, and very flexible.