[inquisitor]

I see. The 800MHz band isn't used in Europe for cellular networks at all, neither for GSM nor UTMS, so the 2100MHz band is the only one useful for Europe.

UMTS is derived from GSM and so there's only a single SIM for both networks, so you will be able to use your 3G-router flawlessly.
Actually GSM and UMTS networks are pretty much integrated and as a result a GSM/UMTS-compatible phone will seamlessly jump (without calls or data sessions dropping) from GSM to UMTS networks and vice versa depending on which network is available.

Since in Europe we have historically established widespread GSM coverage and all UMTS phones sold here are also GSM-compatible, network operators do not provide a 100%-coverage with UMTS. UMTS is rather used as an overlay on GSM-coverage in urban areas. While in Japan UMTS networks are designed to cover the whole country because the 2G "PDC"-network has been switched off this year, in Europe we still keep our 2G GSM networks alive and so network planners still leave places only covered by GSM here and there. Such (small) places (especially indoors) may even occur in urban areas where it's uneconomical to install a UMTS basestation while GSM-coverage suffices. So e.g. you may have only GSM coverage at your hotel room or in the metro.
That's why you should expect dead zones when using a UMTS-only device in Europe. In Austria there's one exception and that's the network operator "3", who as the only Austrian operator does operate only a UMTS network but no GSM network - they probably have less dead zones in urban areas than other operators may have.
But perhaps your 3G-router is GSM-compatible (like more and more Japanese phones become). If you told us the make and model we could check this out.