I work in the animation industry where taking pictures of hand drawn cels and artwork was part of the job (not so much anymore with the arise of computers).
Your best route to quality and preservation is to take the portrait to a service and get it digitally scanned for three reasons:
1) Photography introduces distortion from the lens (barreling, pinching, chromatic aberration, focus loss, ...) or from the lights (reflections, glare, shadow, ...).
2) scanning can be done with uniform lighting, focus, and color temperature to all parts of the portrait. No worries of light loss in the corners as is common with lenses or shadows from less than perfect lighting.
3) You can scan at much higher resolutions and pixel densities than using your camera. Serves as a better master for future prints and alterations. You always want your master to be of greater fidelity than your published output. This allows you to make corrections and alterations without losing quality.
Yes, scanning can be expensive, but if you really care it's the way to go.
If you insist on using your camera, here's how the time tested animation studios did it on all features and shorts using Oxberry and ACME camera systems. You should be able to get close using today's modern advances:
1) Place artwork on flat table large enough to hold the item without folds or bends.
2) You want as much illumination as possible - enough to stop down the lens to at least f16, but more would be better. Stopping down the lens increases sharpness because the aperature filters out stray light rays which cause glare and helps minimize subtle differences in uneven lighting. Improves color contrast as well as paint tends to reflect light differently depending on type of paint used, the color, and brush stroke angle(s) and thickness. Today's paints are largely synthetic and very uniform, but paints from yester year have a lot of variance in pigment and reflectivity which gives portraits nice character you don't get today. It should be a priority to capture those differences.
3) Illumination needs to be color neutral. If it isn't, put gels over the lights (preferred over filters in the camera lens). Ideally, lights should also be covered with polarized gels to minimize glare and reflections. Do not use umbrellas.
Most animation stands use at least 4 lights, 2 on the left, 2 on the right side of the artwork. Using fewer lights usually results in light loss in the corners or shadows. all lights should be the same height, be aimed at near side of the center line of the artwork relative to the light, and symmetrically places about the table. The angle formed from the camera lens, to center of artwork, to lightbulb should be 45 degrees for optimal reflectance.
You can rent lights from a photography store or video/audio center where professional gear is sold. If you live near a college or film school, you may be able to borrow them under certain conditions...especially if you know a student to attends. In some cases, they'll do the picture for you for free.
4) Camera should be mounted directly above the artwork and centered. Use a normal/prime lens or mild telephoto. Wide angle lenses add distortion. Telephoto lenses tend to lack sharpness and contrast.
5) If available, place a heavy plate of color neutral and distortion-free glass over the artwork to press it down and keep flat. This was called a "platen" on animation stands and it's purpose was to eliminate uneven lighting from rumpled artwork as well as force the artwork flat so as to minimize reflections into the lens.
6) Build a camera lens mask (shade/hood). Serves 2 purposes - first purpose is to prevent illumination from the lighting system from entering the lens directly. Second purpose is to keep the background behind the camera from reflecting onto the artwork and creating shadows/highlights or bounced reflections known as 'imprinting' - many people overlook this part.
You can build a cheap mask with a sheet of stiff cardboard or foamcore and cut a hole into the center for the lens of the camera to see through (not poke through). You want to keep the mask a few inches in front of the camera lens. The side of the cardboard facing the artwork should be 100% black and light absorbing. Ideally, glue a sheet of velvet over the cardboard as velvet absorbs light. The mask should be large enough to account for any light coming from behind the camera leaking onto the artwork (ceiling reflection, for example). Mask size is proportional to artwork size and it's distance to the camera. The larger the artwork and/or the further away from the camera, the larger the mask needs to be. You should be able to visually inspect this by looking through the lens of the camera and see if reflections make it onto the artwork - test by putting pure white paper on the table in place of the artwork covered by a piece of glass. If you see reflections of the camera in the result image, then you need to make adjustments to your mask and/or lighting arrangement.
7) taking the picture - if the artwork has lots of bright colors such as yellows/whites/metallics, then stop down the lens an additional half to full stop beyond the light meter's reading as the bright colors will create a glare/haze in the final exposure.
Granted, you may not have the space or equipment to pull this off as described, but it illustrates how a proper setup works so you can make appropriate substitutions where needed.