I have never actually seen a live Hawthorn Jewel Beetle Agrilus sinuatus though I have recorded the species on a dozen occasions. It can be found over a wide area of southern England (map here) by looking at mature hawthorns where the D-shaped exit-holes are a tell-tale sign. The D-shape matches the cross-section of the adult jewel beetle: flattened on top and convex below. The holes are best looked for on lower branches that are dying back but can also be found on the trunk and major boughs.
To be extra sure you have found Agrilus sinuatus exit-holes, you can whittle away the bark to reveal the vacated larval borings which seem to always have quite a regular snaky, zig-zag pattern. The larval borings are also illustrated in a note by Keith Alexander (1990) who pioneered the recording of jewel beetles in this way: available online here. I would like to think that the ‘sinuatus’ of the name (given by Olivier in 1790) refers to the sinuate pattern of the larval borings.
Finding adults in the field must require some luck. They may be very short-lived, they may spend their lives out of reach around the crowns of hawthorns, or they may be too flighty to simply tap them out onto a beating tray. Agrilus sinuatus was regarded as ‘very rare’ by Fowler in 1890, as Vulnerable (RDB2) in 1987, and was downgraded to Nationally Scarce (Na) in 1992 and although still officially Na today we can probably safely call it common, largely thanks to a better understanding of how to spot the signs.
The best way to see adults would presumably be to rear them out of a suitable hawthorn branch. Under natural conditions, adults are active from mid-June to late September so collecting a branch any time up to mid-June ought to do it. The trick would be to find a branch that doesn’t yet have any D-shaped holes in it but looks like it will do soon!
Alexander, K.N.A. (1990). Agrilus sinuatus (Olivier) (Coleoptera: Buprestidae) widespread in Gloucestershire, and at a Herefordshire locality. British journal of entomology and natural history, 3: 31 – 32. [Browse this article online here].