For UV-Visible Spectroscopy, you can prepare the dispersion of silver nanoparticles and perform the analysis. However, for TEM analysis, it depends upon your need of results. You can perform the analysis of silver nanoparticles as you have, as well as dispersing its solution and then drying it.
For silver nanoparticle (AgNPs) work, UV-Vis spectral analysis experiment is carried out to find out the Surface Plasmon Resonance (SPR) peak and I suggest you to perform the spectral analysis in the wavelength of 400-800 nm at a resolution of 1 nm in order to find the SPR peak of AgNPs.
The morphology (size and shape) of AgNPs are used to determined using TEM or high-resolution transmission electron microscopy (HRTEM) for both the equipment you can also find their energy dispersive X-ray spectroscopy (EDX) analysis. The sample is prepared by drop-casting of your AgNPs solution onto a carbon-coated copper TEM grid.
You can find the detailed methodology for both UV-vis and TEM in the below mentioned manuscript published in 2018
Cellular imaging and bactericidal mechanism of green-synthesized silver nanoparticles against human pathogenic bacteria. Journal of Photochemisty and Photobiology B: Biology (2018). 178, 259-269. doi: 10.1016/j.jphotobiol.2017.11.001
There are many reports on synthesizing of Ag NPs in the literature. You can see the common methods for characterization of these nanoparticles in the reported papers as mentioned above.
The surface plasmon resonance peak region of Ag nanoparticles is usually around 400 nm, although this is affected by the particle size and morphology. Thus regards Sathish Sundar's 400-800 nm suggested wavelength range, I will suggest a little more lower wavelength boundary of at least 300 nm.