Start by picking through the samphire to remove roots and any obvious tough stems. Wash and rinse it thoroughly to get rid of any grit, mud or sand, and break up larger, multi-branched stems into smaller pieces. You can expect to lose anything up to a quarter of the samphire in the cleaning and trimming... unless, of course, it's early season (June in the northern hemisphere) and the samphire is particularly tender, in which case you may lose almost none.
Bring to the boil a large pan of fresh, unsalted water, drop in the samphire and cook for three to four minutes. Drain, toss with the butter and olive oil, and season with freshly ground pepper. Serve immediately with lemon wedges, alongside a good piece of grilled or poached fish.